Question

The vertices of a Δ ABC are A(3, 8), B(–1, 2) and C(6, –6). Find:

1. Slope of BC.
2. Equation of a line perpendicular to BC and passing through A.

Answer 1

Given:

A (3, 8), B(–1, 2), C(6, –6)

(i) Slope of BC = `(y_2 - y_1) /(x_2 - x_1)`

Slope of BC = `(-6 - 2)/(6 - (-1))

∴ Slope of BC = `(-8)/7`

(ii) Slope of the line perpendicular to BC:

= `(-1)/((-8/7))`

= `7/8`

Required line ⇒ y − y₁ = m(x − x₁ )

`y - 8 = 7/8(x - 3)`

8y − 64 = 7x − 21

7x − 8y + 43 = 0

Hence, the slope of BC = `(-8)/7` and the equation of a line perpendicular to BC and passing through A is 7x − 8y + 43 = 0.