Question

Points A(x, y), B(3, –2) and C(4, –5) are collinear. The value of y in terms of x is ______.

Options

• 3x – 11

• 11 – 3x

• 3x – 7

• 7 – 3x

Answer 1

Points A(x, y), B(3, –2) and C(4, –5) are collinear. The value of y in terms of x is 7 – 3x.

Explanation:

Points A(x, y), B(3, –2) and C(4, –5) are collinear.

Then, the area of the triangle formed by those points will be zero

∴ `1/2|(x, y, 1),(3, -2, 1),(4, -5, 1)|` = 1

`\implies` x(– 2 + 5) – y(3 – 4) + 1(– 15 + 8) = 0

`\implies` 3x + y – 7 =0

`\implies` y = 7 – 3x