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

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

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Let the points (1, 5), (2, 3) and (– 2, – 11) be representing the vertices A, B, and C of the given triangle respectively.

A = (1,5),\ B = (2,3),\ C = (-2,-11)

Therefore, 

AB = \sqrt{(1-2)^2+(5-3)^2} = \sqrt{5}

BC = \sqrt{(2-(-2))^2+(3-(-11))^2} = \sqrt{4^2+14^2} = \sqrt{16+196} = \sqrt{212}CA = \sqrt{(1-(-2))^2+(5-(-11))^2} = \sqrt{3^2+16^2} = \sqrt{9+256} = \sqrt{265}Since these are not satisfied.

AB+BC \neq CA

BA+AC \neq BC

BC+CA \neq BA

As these cases are not satisfied.

Hence the points are not collinear.

Posted by

Divya Prakash Singh

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