Question

Plot the following points on the same graph paper and check whether they are collinear or not:

(1, 2), (0, 0) and (–1, –2)

Answer 1

Given: (1, 2), (0, 0) and (–1, –2).

Step-wise calculation:

1. Compute slope between (0, 0) and (1, 2):

Slope = `(2 - 0)/(1 - 0)`

= 2

2. Compute slope between (0, 0) and (–1, –2):

Slope = `(-2 - 0)/(-1 - 0)`

= `(-2)/(-1)`

= 2

3. Since the slopes of the segments joining the origin to the other two points are equal both 2, all three points lie on the same straight line.

4. The line through these points has equation y = 2x.

Check: For x = 1 ⇒ y = 2

For x = –1 ⇒ y = –2

For x = 0 ⇒ y = 0

The points (1, 2), (0, 0) and (–1, –2) are collinear they lie on the line y = 2x.