Show that the points A(6, 4), B(9, 7) and C(11, 9) are collinear.

Distance between 2 points (x₁, y₁) and (x₂, y₂) = $\sqrt{(x$2 - x1)^2 + (y2 - y1)^2}

Distance between A(6, 4) and B(9, 7) =

$= \sqrt{(9 - 6)^2 + (7 - 4)^2}\\[1em] = \sqrt{3^2 + 3^2}\\[1em] = \sqrt{9 + 9}\\[1em] = \sqrt{18}\\[1em] = 3\sqrt{2}$

Distance between B(9, 7) and C(11, 9) =

$= \sqrt{(11 - 9)^2 + (9 - 7)^2}\\[1em] = \sqrt{2^2 + 2^2}\\[1em] = \sqrt{4 + 4}\\[1em] = \sqrt{8}\\[1em] = 2\sqrt{2}$

Distance between A(6, 4) and C(11, 9) =

$= \sqrt{(11 - 6)^2 + (9 - 4)^2}\\[1em] = \sqrt{5^2 + 5^2}\\[1em] = \sqrt{25 + 25}\\[1em] = \sqrt{50}\\[1em] = 5\sqrt{2}$

⇒ AB + BC = $3\sqrt{2} + 2\sqrt{2} = 5\sqrt{2}$ = AC

Hence, the points A(6, 4), B(9, 7) and C(11, 9) are collinear.