Question

$A(5,4),B(-3,-2)$ and $C(1,-8)$ are the vertices of a triangle ABC. Find:
(i) The slope of the altitude of AB.

Answer 1

Given: $A(5,4),B(-3,-2)$ and $C(1,-8)$ are the vertices of a triangle ABC.

$\because \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\therefore \text{Slope of AB}=\frac{-2-4}{-3-5}$

$=\frac{-6}{-8}$

$=\frac{3}{4}$

We know that, if two lines are perpendicular, the product of their slopes is $-1$.
Slope of the altitude of AB $=\frac{-1}{\text{slope of}AB}$

$=\frac{-1}{\frac{3}{4}}$

$=\frac{-4}{3}$
Hence, the slope of the altitude of AB is $\frac{-4}{3}$.