Question

show that the points (0,-2) , (-1,1) , (-2,4) are collinear

Answer 1

Let A ≡ (0, -2), B ≡ (-1, 1), C ≡ (-2, 4).

If slope of AB = slope of AC, then it will mean that AB || AC. But A is the common point. So, AB and AC will be the same line. And therefore the three points will be collinear.

Slope = (y1 - y2) / (x1 - x2)

Slope of AB = (- 2 - 1) / (0 + 1)

                    = -3 / 1

                    = -3

Slope of BC = (1 - 4) / (-1 + 2)

                    = -3 / 1

                    = -3

As slope of AB = slope of BC, the three points are collinear.

Hope this helps! :)