Question

If the points P(1, 2), Q(0, 0) and R(x, y) are collinear, then find the relation between x and y.

Given points are P(1, 2), Q(0, 0) and R(x, y).

The given points are collinear, so the area of the triangle formed by them is `square`.

∴ `1/2 |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = square`

`1/2 |1(square) + 0(square) + x(square)| = square`

`square + square + square` = 0

`square + square` = 0

`square = square`

Hence, the relation between x and y is `square`.

Answer 1

Given points are P(1, 2), Q(0, 0) and R(x, y).

The given points are collinear, so the area of the triangle formed by them is zero.

∴ `1/2 |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|` = 0

`1/2` |1(0 – y) + 0(y – 2) + x(2 – 0)| = 0

– y + 0 + 2x = 0

– y + 2x = 0

2x = y

Hence, the relation between x and y is 2x = y.