Question

Find a relation between x and y, if the points A(x, y), B(1, 2) and C(7, 0) are collinear.

Answer 1

Given: Points A(x, y), B(1, 2) and C(7, 0) are collinear.

Slope of BC = `(0 - 2)/(7 - 1)`

= `(-2)/6`

= `(-1)/3`

For A to be collinear with B and C, slope of AB = `(y - 2)/(x - 1)` must equal `−1/3`.

So, `(y - 2)/(x - 1) = -1/3`

Cross-multiply: 3(y – 2) = –(x – 1)

3y – 6 = –x + 1

Rearranging: x + 3y – 7 = 0

The relation between x and y is x + 3y – 7 = 0 (equivalently `y = (7 − x)/3`).