Prove that the line through A(–2, 6) and B(4, 8) is perpendicular to the line through C(8, 12) and D(4, 24).

The slope of the line passing through two points (x₁, y₁) and (x₂, y₂) is given by

Slope = $\dfrac{y$2 - y1}{x2 - x1}

Slope (m₁) of line joining (-2, 6) and (4, 8) is,

= $\dfrac{8 - 6}{4 - (-2)} = \dfrac{2}{6} = \dfrac{1}{3}$

Slope (m₂) of line joining (8, 12) and (4, 24) is,

=$\dfrac{24 - 12}{4 - 8} = \dfrac{12}{-4} = -3$

m₁ × m₂ = $\dfrac{1}{3} \times -3$ = -1.

Product of slopes = -1.

Hence, the lines are perpendicular to each other.