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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.

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nobillionaireNobley
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.
fichoh

The points A, B and C are not collinear.

  • Two or more points may be colinear if they lie on a single straight line.

Given the points A, B, and C :

  • AB = 7 ; BC = 4 ; AC = 9

If B is in between A and C ; then :

  • AB + BC = AC

Hence,

  • 7 + 4 = 11

However, the length of AC = 9 and not 11 ;

  • This shows that the three points, AB, BC and AC are not on a single straight line and hence, not collinear.

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