In the previous section we saw the procedure for locating points in the cartesian plane. In this section we will see a few solved examples.
Solved example 31.1
Observe the fig.31.8 below and complete the following statements:
(a) The abscissa and ordinate of the point B are ___ and ___ respectively. Hence, the coordinates of B are (___ , ___)
(b) The x-coordinate and y-coordinate of the point M are ___ and ___ respectively. Hence, the coordinates of M are (___ , ___)
(c) The x-coordinate and y-coordinate of the point L are ___ and ___ respectively. Hence, the coordinates of L are (___ , ___)
(d) The x-coordinate and y-coordinate of the point S are ___ and ___ respectively. Hence, the coordinates of S are (___ , ___)
Solution:
(a) Let us apply the rules to point B:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of B from the y-axis (measured along the x-axis) is '4 units'
♦ It is measured along OX. So it is positive
♦ Thus the x-coordinate of B is '4'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of B from the x-axis (measured along the y-axis) is '3 units'
♦ It is measured along OY. So it is positive
♦ Thus the y-coordinate of B is '3'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of B are: (4,3)
(b) Let us apply the rules to point M:
(i) Applying the first rule to find the x-coordinate:
• Perpendicular distance of M from the y-axis (measured along the x-axis) is '3 units'
♦ It is measured along OX'. So it is negative
♦ Thus the x-coordinate of M is '-3'
(ii) Applying the second rule to find the y-coordinate:
• Perpendicular distance of M from the x-axis (measured along the y-axis) is '4 units'
♦ It is measured along OY. So it is positive
♦ Thus the y-coordinate of M is '4'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of M are: (-3,4)
(c) Let us apply the rules to point L:
(i) Applying the first rule to find the x-coordinate:
• Perpendicular distance of L from the y-axis (measured along the x-axis) is '5 units'
♦ It is measured along OX'. So it is negative
♦ Thus the x-coordinate of L is '-5'
(ii) Applying the second rule to find the y-coordinate:
• Perpendicular distance of L from the x-axis (measured along the y-axis) is '4 units'
♦ It is measured along OY'. So it is negative
♦ Thus the y-coordinate of L is '-4'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of L are: (-5,-4)
(d) Let us apply the rules to point S:
(i) Applying the first rule to find the x-coordinate:
• Perpendicular distance of S from the y-axis (measured along the x-axis) is '3 units'
♦ It is measured along OX. So it is positive.
♦ Thus the x-coordinate of S is '3'
(ii) Applying the second rule to find the y-coordinate:
• Perpendicular distance of S from the x-axis (measured along the y-axis) is '4 units'
♦ It is measured along OY'. So it is negative
♦ Thus the y-coordinate of S is '-4'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of S are: (3,-4)
Solved example 31.2
In the fig.31.9 below, some points are marked on the axes itself. Write the coordinates of each of them. Given that, point E is at a distance of 2⁄3 units from the origin.
Solution:
(a) Let us apply the rules to point A:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of A from the y-axis (measured along the x-axis) is '4 units'
♦ It is measured along OX. So it is positive
♦ Thus the x-coordinate of A is '4'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of A from the x-axis is '0 units'
♦ We cannot say that is measured along any particular direction. Because there is no measurement to take. '0 units' is neither positive nor negative
♦ Thus the y-coordinate of A is '0'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of A are: (4,0)
(b) Let us apply the rules to point B:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of B from the y-axis is '0 units'
♦ We cannot say that is measured along any particular direction. Because there is no measurement to take. '0 units' is neither positive nor negative
♦ Thus the x-coordinate of B is '0'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of B from the x-axis (measured along the y-axis) is '3 units'
♦ It is measured along OY. So it is positive
♦ Thus the y-coordinate of B is '3'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of B are: (0,3)
(c) Let us apply the rules to point C:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of C from the y-axis (measured along the x-axis) is '5 units'
♦ It is measured along OX'. So it is negative
♦ Thus the x-coordinate of C is '-5'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of C from the x-axis is '0 units'
♦ We cannot say that is measured along any particular direction. Because there is no measurement to take. '0 units' is neither positive nor negative
♦ Thus the y-coordinate of C is '0'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of C are: (-5,0)
(d) Let us apply the rules to point D:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of D from the y-axis is '0 units'
♦ We cannot say that is measured along any particular direction. Because there is no measurement to take. '0 units' is neither positive nor negative
♦ Thus the x-coordinate of D is '0'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of D from the x-axis (measured along the y-axis) is '4 units'
♦ It is measured along OY'. So it is negative
♦ Thus the y-coordinate of D is '-4'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of D are: (0,-4)
(e) Let us apply the rules to point E:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of E from the y-axis (measured along the x-axis) is '2⁄3 units'
♦ It is measured along OX. So it is positive
♦ Thus the x-coordinate of E is '2⁄3'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of E from the x-axis is '0 units'
♦ We cannot say that is measured along any particular direction. Because there is no measurement to take. '0 units' is neither positive nor negative
♦ Thus the y-coordinate of E is '0'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of E are: (2⁄3,0)
■ The coordinates of all points on the x-axis will be of the form: (±x,0)
♦ Use '+' sign if the point lies on OX
♦ Use '-' sign if the point lies on OX'
• If a point is on the y-axis, it's x-coordinate will be zero. That is:
■ The coordinates of all points on the y-axis will be of the form: (0,±y)
♦ Use '+' sign if the point lies on OY
♦ Use '-' sign if the point lies on OY'
• Now we can consider the origin
♦ The distance of O from the x-axis is 0
♦ The distance of O from the y-axis is 0
■ So the coordinates of the origin will always be: (0,0)
From the above two solved examples, we get the following information:
1. If a point lies in the first quadrant,
• it's x-coordinate will be positive
• it's y-coordinate will be positive
• It is enclosed between the positive OX and positive OY
■ So it's coordinates will be of the form (+,+)
2. If a point lies in the second quadrant,
• it's x-coordinate will be negative
• it's y-coordinate will be positive
• It is enclosed between the negative OX' and positive OY
■ So it's coordinates will be of the form (-,+)
3. If a point lies in the third quadrant,
• it's x-coordinate will be negative
• it's y-coordinate will be negative
• It is enclosed between the negative OX' and negative OY'
■ So it's coordinates will be of the form (-,-)
4. If a point lies in the fourth quadrant,
• it's x-coordinate will be positive
• it's y-coordinate will be negative
• It is enclosed between the positive OX and positive OY'
■ So it's coordinates will be of the form (+,-)
This is shown in the fig.31.10 below:
Solved example 31.3
Observe the fig.31.11 below and write the following:
1. The coordinates of B
2. The coordinates of C
3. The point identified by the coordinates (-3,-5)
4. The point identified by the coordinates (2,-4)
5. The abscissa of point D
6. The ordinate of point H
7. The coordinates of point H
8. The coordinates of point M
Solution:
(1) Let us apply the rules to point B:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of B from the y-axis (measured along the x-axis) is '5 units'
♦ It is measured along OX'. So it is negative
♦ Thus the x-coordinate of B is '-5'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of B from the x-axis (measured along the y-axis) is '2 units'
♦ It is measured along OY. So it is positive
♦ Thus the y-coordinate of B is '2'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of B are: (-5,2)
(2) Let us apply the rules to point C:
(i) Applying the first rule to find the x-coordinate:
• Perpendicular distance of C from the y-axis (measured along the x-axis) is '5 units'
♦ It is measured along OX. So it is positive
♦ Thus the x-coordinate of C is '5'
(ii) Applying the second rule to find the y-coordinate:
• Perpendicular distance of C from the x-axis (measured along the y-axis) is '5 units'
♦ It is measured along OY'. So it is negative
♦ Thus the y-coordinate of B is '-5'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of C are: (-5,-5)
(3) The given coordinates are (-3,-5)
• Here both the x and y coordinates are negative. So the point will be in the third quadrant
• So we need to consider H and E only. The required answer will be one among them
• The given x coordinate is '-3'. So the required point will be at a distance of 3 units from the y-axis
♦ H is at a distance of 5 units from the y axis
♦ E is at a distance of 3 units from the y axis
• So the required point must be E
• To confirm, let us check the given y coordinate. It is '-5'
• E is indeed at a distance of 5 units from the x-axis.
• So E is our required point
(4) The given coordinates are (2,-4)
• Here the x coordinate is positive and y coordinate is negative. So the point will be in the fourth quadrant
• So we need to consider G and C only. The required answer will be one among them
• The given x coordinate is '2'. So the required point will be at a distance of 2 units from the y-axis
♦ G is at a distance of 2 units from the y axis
♦ C is at a distance of 5 units from the y axis
• So the required point must be G
• To confirm, let us check the given y coordinate. It is '-4'
• G is indeed at a distance of 4 units from the x-axis.
• So G is our required point
(5) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of D from the y-axis (measured along the x-axis) is '6 units'
♦ It is measured along OX. So it is positive
♦ Thus the x-coordinate (abscissa) of D is '6'
(6) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of H from the x-axis (measured along the y-axis) is '3 units'
♦ It is measured along OY'. So it is negative
♦ Thus the y-coordinate (ordinate) of B is '-3'
(7) Let us apply the rules to point L:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of L from the y-axis is '0 units'
♦ We cannot say that is measured along any particular direction. Because there is no measurement to take. '0 units' is neither positive nor negative
♦ Thus the x-coordinate of L is '0'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of L from the x-axis (measured along the y-axis) is '5 units'
♦ It is measured along OY. So it is positive
♦ Thus the y-coordinate of L is '5'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of L are: (0,5)
(8) Let us apply the rules to point M:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of M from the y-axis (measured along the x-axis) is '3 units'
♦ It is measured along OX'. So it is negative
♦ Thus the x-coordinate of M is '-3'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of M from the x-axis is '0 units'
♦ We cannot say that is measured along any particular direction. Because there is no measurement to take. '0 units' is neither positive nor negative
♦ Thus the y-coordinate of M is '0'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of M are: (-3,0)
Solved example 31.1
Observe the fig.31.8 below and complete the following statements:
 |
| Fig.31.8 |
(b) The x-coordinate and y-coordinate of the point M are ___ and ___ respectively. Hence, the coordinates of M are (___ , ___)
(c) The x-coordinate and y-coordinate of the point L are ___ and ___ respectively. Hence, the coordinates of L are (___ , ___)
(d) The x-coordinate and y-coordinate of the point S are ___ and ___ respectively. Hence, the coordinates of S are (___ , ___)
Solution:
(a) Let us apply the rules to point B:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of B from the y-axis (measured along the x-axis) is '4 units'
♦ It is measured along OX. So it is positive
♦ Thus the x-coordinate of B is '4'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of B from the x-axis (measured along the y-axis) is '3 units'
♦ It is measured along OY. So it is positive
♦ Thus the y-coordinate of B is '3'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of B are: (4,3)
(b) Let us apply the rules to point M:
(i) Applying the first rule to find the x-coordinate:
• Perpendicular distance of M from the y-axis (measured along the x-axis) is '3 units'
♦ It is measured along OX'. So it is negative
♦ Thus the x-coordinate of M is '-3'
(ii) Applying the second rule to find the y-coordinate:
• Perpendicular distance of M from the x-axis (measured along the y-axis) is '4 units'
♦ It is measured along OY. So it is positive
♦ Thus the y-coordinate of M is '4'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of M are: (-3,4)
(c) Let us apply the rules to point L:
(i) Applying the first rule to find the x-coordinate:
• Perpendicular distance of L from the y-axis (measured along the x-axis) is '5 units'
♦ It is measured along OX'. So it is negative
♦ Thus the x-coordinate of L is '-5'
(ii) Applying the second rule to find the y-coordinate:
• Perpendicular distance of L from the x-axis (measured along the y-axis) is '4 units'
♦ It is measured along OY'. So it is negative
♦ Thus the y-coordinate of L is '-4'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of L are: (-5,-4)
(d) Let us apply the rules to point S:
(i) Applying the first rule to find the x-coordinate:
• Perpendicular distance of S from the y-axis (measured along the x-axis) is '3 units'
♦ It is measured along OX. So it is positive.
♦ Thus the x-coordinate of S is '3'
(ii) Applying the second rule to find the y-coordinate:
• Perpendicular distance of S from the x-axis (measured along the y-axis) is '4 units'
♦ It is measured along OY'. So it is negative
♦ Thus the y-coordinate of S is '-4'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of S are: (3,-4)
Solved example 31.2
In the fig.31.9 below, some points are marked on the axes itself. Write the coordinates of each of them. Given that, point E is at a distance of 2⁄3 units from the origin.
 |
| Fig.31.9 |
(a) Let us apply the rules to point A:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of A from the y-axis (measured along the x-axis) is '4 units'
♦ It is measured along OX. So it is positive
♦ Thus the x-coordinate of A is '4'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of A from the x-axis is '0 units'
♦ We cannot say that is measured along any particular direction. Because there is no measurement to take. '0 units' is neither positive nor negative
♦ Thus the y-coordinate of A is '0'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of A are: (4,0)
(b) Let us apply the rules to point B:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of B from the y-axis is '0 units'
♦ We cannot say that is measured along any particular direction. Because there is no measurement to take. '0 units' is neither positive nor negative
♦ Thus the x-coordinate of B is '0'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of B from the x-axis (measured along the y-axis) is '3 units'
♦ It is measured along OY. So it is positive
♦ Thus the y-coordinate of B is '3'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of B are: (0,3)
(c) Let us apply the rules to point C:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of C from the y-axis (measured along the x-axis) is '5 units'
♦ It is measured along OX'. So it is negative
♦ Thus the x-coordinate of C is '-5'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of C from the x-axis is '0 units'
♦ We cannot say that is measured along any particular direction. Because there is no measurement to take. '0 units' is neither positive nor negative
♦ Thus the y-coordinate of C is '0'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of C are: (-5,0)
(d) Let us apply the rules to point D:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of D from the y-axis is '0 units'
♦ We cannot say that is measured along any particular direction. Because there is no measurement to take. '0 units' is neither positive nor negative
♦ Thus the x-coordinate of D is '0'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of D from the x-axis (measured along the y-axis) is '4 units'
♦ It is measured along OY'. So it is negative
♦ Thus the y-coordinate of D is '-4'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of D are: (0,-4)
(e) Let us apply the rules to point E:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of E from the y-axis (measured along the x-axis) is '2⁄3 units'
♦ It is measured along OX. So it is positive
♦ Thus the x-coordinate of E is '2⁄3'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of E from the x-axis is '0 units'
♦ We cannot say that is measured along any particular direction. Because there is no measurement to take. '0 units' is neither positive nor negative
♦ Thus the y-coordinate of E is '0'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of E are: (2⁄3,0)
Based on the results from the above solved example 31.2, we can write the following:
• If a point is on the x-axis, it's y-coordinate will be zero. That is:■ The coordinates of all points on the x-axis will be of the form: (±x,0)
♦ Use '+' sign if the point lies on OX
♦ Use '-' sign if the point lies on OX'
• If a point is on the y-axis, it's x-coordinate will be zero. That is:
■ The coordinates of all points on the y-axis will be of the form: (0,±y)
♦ Use '+' sign if the point lies on OY
♦ Use '-' sign if the point lies on OY'
• Now we can consider the origin
♦ The distance of O from the x-axis is 0
♦ The distance of O from the y-axis is 0
■ So the coordinates of the origin will always be: (0,0)
1. If a point lies in the first quadrant,
• it's x-coordinate will be positive
• it's y-coordinate will be positive
• It is enclosed between the positive OX and positive OY
■ So it's coordinates will be of the form (+,+)
2. If a point lies in the second quadrant,
• it's x-coordinate will be negative
• it's y-coordinate will be positive
• It is enclosed between the negative OX' and positive OY
■ So it's coordinates will be of the form (-,+)
3. If a point lies in the third quadrant,
• it's x-coordinate will be negative
• it's y-coordinate will be negative
• It is enclosed between the negative OX' and negative OY'
■ So it's coordinates will be of the form (-,-)
4. If a point lies in the fourth quadrant,
• it's x-coordinate will be positive
• it's y-coordinate will be negative
• It is enclosed between the positive OX and positive OY'
■ So it's coordinates will be of the form (+,-)
This is shown in the fig.31.10 below:
 |
| Fig.31.10 |
Observe the fig.31.11 below and write the following:
1. The coordinates of B
2. The coordinates of C
3. The point identified by the coordinates (-3,-5)
4. The point identified by the coordinates (2,-4)
5. The abscissa of point D
6. The ordinate of point H
7. The coordinates of point H
8. The coordinates of point M
(1) Let us apply the rules to point B:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of B from the y-axis (measured along the x-axis) is '5 units'
♦ It is measured along OX'. So it is negative
♦ Thus the x-coordinate of B is '-5'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of B from the x-axis (measured along the y-axis) is '2 units'
♦ It is measured along OY. So it is positive
♦ Thus the y-coordinate of B is '2'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of B are: (-5,2)
(2) Let us apply the rules to point C:
(i) Applying the first rule to find the x-coordinate:
• Perpendicular distance of C from the y-axis (measured along the x-axis) is '5 units'
♦ It is measured along OX. So it is positive
♦ Thus the x-coordinate of C is '5'
(ii) Applying the second rule to find the y-coordinate:
• Perpendicular distance of C from the x-axis (measured along the y-axis) is '5 units'
♦ It is measured along OY'. So it is negative
♦ Thus the y-coordinate of B is '-5'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of C are: (-5,-5)
(3) The given coordinates are (-3,-5)
• Here both the x and y coordinates are negative. So the point will be in the third quadrant
• So we need to consider H and E only. The required answer will be one among them
• The given x coordinate is '-3'. So the required point will be at a distance of 3 units from the y-axis
♦ H is at a distance of 5 units from the y axis
♦ E is at a distance of 3 units from the y axis
• So the required point must be E
• To confirm, let us check the given y coordinate. It is '-5'
• E is indeed at a distance of 5 units from the x-axis.
• So E is our required point
(4) The given coordinates are (2,-4)
• Here the x coordinate is positive and y coordinate is negative. So the point will be in the fourth quadrant
• So we need to consider G and C only. The required answer will be one among them
• The given x coordinate is '2'. So the required point will be at a distance of 2 units from the y-axis
♦ G is at a distance of 2 units from the y axis
♦ C is at a distance of 5 units from the y axis
• So the required point must be G
• To confirm, let us check the given y coordinate. It is '-4'
• G is indeed at a distance of 4 units from the x-axis.
• So G is our required point
(5) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of D from the y-axis (measured along the x-axis) is '6 units'
♦ It is measured along OX. So it is positive
♦ Thus the x-coordinate (abscissa) of D is '6'
(6) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of H from the x-axis (measured along the y-axis) is '3 units'
♦ It is measured along OY'. So it is negative
♦ Thus the y-coordinate (ordinate) of B is '-3'
(7) Let us apply the rules to point L:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of L from the y-axis is '0 units'
♦ We cannot say that is measured along any particular direction. Because there is no measurement to take. '0 units' is neither positive nor negative
♦ Thus the x-coordinate of L is '0'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of L from the x-axis (measured along the y-axis) is '5 units'
♦ It is measured along OY. So it is positive
♦ Thus the y-coordinate of L is '5'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of L are: (0,5)
(8) Let us apply the rules to point M:
(i) Applying the first rule to find the x-coordinate (abscissa):
• Perpendicular distance of M from the y-axis (measured along the x-axis) is '3 units'
♦ It is measured along OX'. So it is negative
♦ Thus the x-coordinate of M is '-3'
(ii) Applying the second rule to find the y-coordinate (ordinate):
• Perpendicular distance of M from the x-axis is '0 units'
♦ We cannot say that is measured along any particular direction. Because there is no measurement to take. '0 units' is neither positive nor negative
♦ Thus the y-coordinate of M is '0'
(iii) Applying the third rule to write down the coordinates:
• x-coordinate first and then the y-coordinate. Inside brackets and separated by comma. We get:
■ The coordinates of M are: (-3,0)
In the next section we will see the method of plotting.
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