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Question

Question 3
Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

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Solution

Let the points (1, 5), (2, 3) and (- 2,-11) be representing the vertices A, B and C of a triangle respectively.
Let A = (1, 5), B = (2, 3) and C = (- 2,-11)
Distance between the points is given by
(x1x2)2+(y1y2)2
AB=(12)2+(53)2=5
BC=(2(2))2+(3(11))2
=42+142=16+196=212
CA=(1(2))2+(5(11))2
=32+162=9+256=265
Since AB+BCCA
Therefore, the points (1, 5), (2, 3), and ( - 2, - 11) are not collinear.

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