# Problems on Plotting Points in the x-y Plane

Here we will learn how to solve different types of problems on plotting points in the x-y plane.

1. Plot the points in the same figure.

(i) (3, -1), (ii) (-5, 0), (iii) (3, 4.5), (iv) (-1, 6), (v) (-2.5, -1.5)

Solution:

Draw two mutually perpendicular lines X’OX and Y’OY which are the x and y axes respectively.

Indicate the numbers (on a certain scale) on both the lines with O and 0.

(i) Let A = (3, -1). Here the x-coordinate = 3 and y-coordinate = -1. So, move 3 units from O towards the positive direction of the x-axis. From that place move 1 unit towards the negative direction of the y-axis. The position of the point now reached has the coordinates (3, -1).

(ii) Let B = (-5, 0). Here, the x-coordinate = -5 and the y-coordinate = 0. So, the point is on the x-axis. Move 5 units from O towards the negative direction of the x-axis. The position of the point reached has the coordinates (-5, 0).

(iii) Let C = (3, 4.5). Here, the x-coordinate = 3 and the y-coordinate = 4.5. So, move 3 units from O towards the positive direction of the x-axis. From that place move 4.5 units towards the positive direction of the y-axis. The position of the point now reached has the coordinates (3, 4.5).

(iv) Let D = (-1, 6). Here, the x-coordinate = -1 and the y-coordinate = 6. So, move 1 unit from O towards the negative direction of the x-axis. From that place move 6 units towards the positive direction of the y-axis. The position of the point now reached has the coordinates (-1, 6).

(v) Let E = (-2.5, -1.5). Here, the x-coordinate = -2.5 and the y-coordinate = -1.5. So, move 2.5 units from O towards the negative direction of the x-axis. From that place move 1.5 units towards the negative direction of the y-axis. The position of the point now reached has the coordinates (-2.5, -1.5).

2. Plot the points (12, -8) and (-16, -20) in the x-y plane.

Solution:

Taking 1 cm = 4 as the scale of representation the points are plotted as shown below.

(i) Let P = (12, -8). Here the x-coordinate = 12 and y-coordinate = -8. So, move 12 units from O towards the positive direction of the x-axis. From that place move 8 units towards the negative direction of the y-axis. The position of the point now reached has the coordinates (12, -8).

(ii) Let Q = (-16, -20). Here, the x-coordinate = -16 and the y-coordinate = -20. So, move 16 units from O towards the negative direction of the x-axis. From that place move 20 units towards the negative direction of the y-axis. The position of the point now reached has the coordinates (-16, -20).