Question

A(– 4, 2), B(6, 4) and C(2, – 2) are the vertices of $$\triangle \mathrm{ABC}$$. Find the equation of altitude BM.

Answer 1

Altitude $$\mathrm{BM}$$ is perpendicular to $$\mathrm{AC}$$.

Slope of $$\mathrm{AC}$$ joining $$\mathrm{A}(-4, 2)$$ and $$\mathrm{C}(2, -2)$$:

$$m_{\mathrm{AC}} = \frac{-2 - 2}{2 - (-4)}$$

$$= \frac{-4}{6}$$

$$= -\frac{2}{3}$$

Slope of $$\mathrm{BM}$$ is $$-\frac{1}{m_{\mathrm{AC}}} = \frac{3}{2}$$.

Passing through $$\mathrm{B}(6, 4)$$:

$$y - 4 = \frac{3}{2}(x - 6)$$

$$2(y - 4) = 3(x - 6)$$

$$2y - 8 = 3x - 18$$

$$3x - 2y - 10 = 0$$