Prove that the line through, (-2, 6) and (4, 8) is perpendicular to the line through (8, 12) and (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,

$= \dfrac{8 - 6}{4 - (-2)} \\[1em] = \dfrac{2}{6} \\[1em] = \dfrac{1}{3}.$

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

$= \dfrac{24 - 12}{4 - 8} \\[1em] = \dfrac{12}{-4} \\[1em] = -3.$

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

Hence, the lines are perpendicular to each other.