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

Collinear means they lie on the same line when connected to each other. In order for you to prove this, the distances between the points have to add up to the length of the line.

AB + BC = AC

7 + 4 ? 9

11 ≠ 9

So since they don't add up, the points are not collinear.

Answer 2

If the points are collinear, then that means they lie on the same line when connected to each other. In order to prove this, the distances between the points must sum up to the length of the line.

AB + BC = AC
7 + 4 ? 9
11 ≠ 9

Since they do not sum up, therefore, the points are not collinear.