Question

Show that the point P (−4, 2) lies on the line segment joining the points A (−4, 6) and B (−4, −6).

Answer 1

We have to show that point P (−4, 2) lies on line segment AB with points A (−4, 6) and

B (−4, −6)

If P (−4, 2) lies on the line segment joining A (−4, 6) and B (−4, −6), then the three points

must be collinear.

Let the three points be not collinear and form a triangle PAB

We know that area of a triangle with coordinates of vertices $(x_1,y_1),(x_2,y_2),(x_3,y_3)$

Since area of the triangle is 0, no triangle exists.

Therefore points P (−4, 2), A (−4, 6) and B (−4, −6) are collinear.