Draw co-ordinate axes and represent the following points :
(i) A(2, 4)
(ii) B(-1, 3)
(iii) C(4, -3)
(iv) D(-3, -4)
(v) E(0, 6)
(vi) F(-2, 0)
Answer
The graph is shown below:
On a graph paper plot the points, A(2, 4), B(-1, 3), C(4, -3), D(-3, -4), E(0, 6), F(-2, 0).
On which axis does the following point lie :
(i) P(3, 0)
(ii) Q(0, 4)
(iii) R(-2, 0)
(iv) S(0, -3)
Answer
We know that,
If the y-coordinate is zero (y = 0), the point lies on the x-axis.
If the x-coordinate is zero (x = 0), the point lies on the y-axis.
(i) P(3, 0)
Here, y-coordinate is 0.
Hence, point P lies on x-axis.
(ii) Q(0, 4)
Here, x-coordinate is 0.
Hence, point Q lies on y-axis.
(iii) R(-2, 0)
Here, y-coordinate is 0.
Hence, point R lies on x-axis.
(iv) S(0, -3)
Here, x-coordinate is 0.
Hence, S lies on y-axis.
Find the distance of each of the following points from x-axis and y-axis :
(i) A(7, 4)
(ii) B(3, -5)
(iii) C(-4, -2)
(iv) D(-3, 6)
Answer
We know that,
Distance from the x-axis is the absolute value of the y-coordinate : |y|.
Distance from the y-axis is the absolute value of the x-coordinate : |x|.
(i) A(7, 4)
Distance from x-axis : |4| = 4 units and distance from y-axis : |7| = 7 units.
Hence, distance from x-axis and y-axis of the point A (7, 4) are 4 units and 7 units respectively.
(ii) B(3, -5)
Distance from x-axis: |-5| = 5 units and distance from y-axis : |3| = 3 units
Hence, distance from x-axis and y-axis of point B(3, -5) are 5 units and 3 units respectively.
(iii) C(-4, -2)
Distance from x-axis: |-2| = 2 units
Distance from y-axis: |-4| = 4 units
Hence, distance from x-axis and y-axis of point C(-4, -2) are 2 units and 4 units respectively.
(iv) D(-3, 6)
Distance from x-axis : |6| = 6 units and distance from y-axis : |-3| = 3 units
Hence, distance from x-axis and y-axis of point D(-3, 6) are 6 units and 3 units respectively.
A point lies on x-axis at a distance of 4 units from y-axis. What are the co-ordinates of this point ?
Answer
If a point lies on the x‑axis, its y‑coordinate is 0.
If it’s at a distance of 4 units from the y‑axis, that means its x-coordinate is 4 or -4.
Its co-ordinates are (4, 0) or (-4, 0).
Hence, co-ordinates of the point are (4, 0) or (-4, 0).
A point lies on y-axis at a distance of 5 units from x-axis. What are the co-ordinates of this point ?
Answer
If a point lies on the y‑axis, its x‑coordinate is 0.
If it’s at a distance of 5 units from the x‑axis, that means its y-coordinate is 5 or -5.
Its co-ordinates are (0, 5) or (0, -5).
Hence, co-ordinates of the point are (0, 5) or (0, -5).
What do you mean by the line :
(i) x = 0
(ii) x = 4
(iii) y = 0
(iv) y = 4
(v) x = -3
(vi) y = -2
Answer
(i) x = 0
This is the equation of the y-axis itself.
(ii) x = 4
This is a vertical line parallel to the y-axis, located 4 units to the right of the y-axis.
(iii) y = 0
This is the equation of the x-axis itself.
(iv) y = 4
This is a horizontal line parallel to the x-axis, located 4 units above the x-axis.
(v) x = -3
This is a vertical line parallel to the y-axis, located 3 units to the left of the y-axis.
(vi) y = -2
This is a horizontal line parallel to the x-axis, located 2 units below the x-axis.