Using the distance formula, show that the points A

Solution:

Given: The 3 points are A(3, -2), B(5, 2) and C(8, 8).

$A B=\sqrt{(5-3)^{2}+(2+2)^{2}}$

$=\sqrt{4+16}$

$=2 \sqrt{5}$ units

$B C=\sqrt{(8-5)^{2}+(8-2)^{2}}$

$=\sqrt{9+36}$

$=3 \sqrt{5}$ units

$A C=\sqrt{(8-3)^{2}+(8+2)^{2}}$

$=\sqrt{25+100}$

$=5 \sqrt{5}$ units …..(3)

From equations 1, 2 and 3, we have

⇒ AC = AB + BC

This is possible only if the points are collinear.

Therefore, the points A, B and C are collinear.

Hence, proved.