Question

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

Answer 1

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

Let, A=(1,5); B=(2, 3); C=(−2, −11)

\(\therefore\) AB=\(\sqrt{(1-2)^2+(5-3)^2}=\sqrt5\)
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, AB+BC\(\neq\)CA

Therefore, the points (1, 5), (2, 3), and (−2, −11) are not collinear.