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 a triangle respectively.
Let A = (1, 5), B = (2, 3) and C = (- 2,-11)
Distance between the points is given by
$\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$
$\therefore AB=\sqrt{{(1-2)}^2+{(5-3)}^2}=\sqrt{5}$
$BC=\sqrt{{(2-(-2))}^2+{(3-(-11))}^2}$
$=\sqrt{4^2+{14}^2}=\sqrt{16+196}=\sqrt{212}$
$AC=\sqrt{{(1-(-2))}^2+{(5-(-11))}^2}$
$=\sqrt{3^2+{16}^2}=\sqrt{9+256}=\sqrt{265}$
Since $AB+BC\ne AC$
Therefore, the points (1, 5), (2, 3), and ( - 2, - 11) are not collinear.