Question

From the given figure, find:

1. the co-ordinates of A, B and C.
2. the equation of the line through A and parallel to BC.

Answer 1

i. A = (2, 3), B = (−1, 2), C = (3, 0)

ii. Slope of BC = `(0-2) /(3+1) = -2/4 = -1/2`

Slope of required line which is parallel to BC = Slope of BC = `-1/2`

(x₁, y₁) = (2, 3)

The required equation of the line through A and parallel to BC is given by:

y – y₁ = m(x – x₁)

`=> y - 3 = -1/2(x - 2)`

`=>` 2y − 6 = −x + 2

`=>` x + 2y − 6 − 2 = 0

`=>` x + 2y − 8 = 0

`=>` x + 2y = 8