Question

Three points, A, B, and C exists in space such that B is "between" A and C. It is known that AB=7, BC=4, and AC=9. Are points A,B, and C collinear? Give a written explanation, supported by mathematical evidence, for your answer.

Answer 1

Two or more points are said to be collinear if they lie on the same straight line.

Given a straight line XY, with a point P on the straight line between point X and Y, then
XP + PY = XY

From the question, it was given that AB = 7 and BC = 4, so if A, B, C are colinear, then
AB + BC = AC
i.e. 7 + 4 = 11

But, from the equation, AC = 9.

Therefore, points A, B and C are not collinear.