Question

prove that the points (0,a) (b\2,a\2) and (b,0) are collinear

Answer 1

To prove that they are collinear, we find the gradient of the point 1 and point 2 and then gradient of the point 2 and point 3. If they are the same, the 3 points are collinear.

Find the gradient of (0, a) and (b/2 , a/2)

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

Gradient =(a/2 - a) / (b/2 - 0)

Gradient = (- 1/2a) /(b/2)

Gradient = - a/b

Find the gradient of (b/2 , a/2) and (b. 0)

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

Gradient =(a/2 - 0) / (b/2 - b)

Gradient =(a/2) / (-b/2)

Gradient = - a/b

Since both the gradient are the same, they are collinear.