Question

Show that the following set of points are collinear.
$(2,5),(4,6)$ and $(8,8)$

Answer 1

Formula:

Area of triangle $=\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$

If the area of a triangle is zero, then the points are collinear.

Given,

$A(2,5),B(4,6),C(8,8)$

Area of $△ABC=\frac{1}{2}\left[2\right(6-8)+4(8-5)+8(5-6\left)\right]$

$=\frac{1}{2}[-4+12-8]$

$=0$sq.units

Hence the given points are collinear