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 √(x1−x2)2+(y1−y2)2 ∴AB=√(1−2)2+(5−3)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+BC≠CA Therefore, the points (1, 5), (2, 3), and ( - 2, - 11) are not collinear.

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