Question

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

1. (–1, –1), (2, 2) and (3, 3)
2. (1, 2), (0, 0) and (–1, –2)

Answer 1

Both sets of points are collinear.

1. Evaluate Set (a)

The point are P₁(–1, –1), P₂(2, 2) and P₃(3, 3)

To check for collinearity, we calculate the slope (m) between pairs of points:

Slope P₁P₂ = `(2 - (-1))/(2 - (-1))`

= `3/3`

= 1

Slope P₂P₃ = `(3 - 2)/(3 - 2)`

= `1/1`

= 1

Since the slopes are equal, the points lie on the line y = x.

2. Evaluate Set (b)

The point are Q₁(1, 2), Q₂(0, 0) and Q₃(–1, –2).

Slope Q₁Q₂ = `(0 - 2)/(0 - 1)`

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

= 2

Slope Q₂Q₃ = `(-2 - 0)/(-1 - 0)`

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

= 2

Since the slopes are equal, these points lie on the line y = 2x.

Both sets of points, (a) (–1, –1), (2, 2), (3, 3) and (b) (1, 2), (0, 0), (–1, –2), are collinear.