Question

If the points A (a, 0), B (0, b) and C (c, 0) are collinear then a = -c.

(a) False

(b) True

I have been asked this question in quiz.

The question is from Geometry in section Coordinate Geometry of Mathematics – Class 10

Answer 1

The correct option is (a) False

For explanation: We know that, area of triangle = \(\frac {1}{2}\){x1(y2 – y3 ) + x2(y3 – y1 ) + x3(y1 – y2 )}

The three points are A (a, 0), B (0, b) and C (c, 0)

Since the points are collinear, the area of triangle will be zero.

The area of triangle = \(\frac {1}{2}\) {a(b – 0) + 0(c – 0) + c(0 – b) } = \(\frac {1}{2}\) {ab + 0 – bc}

\(\frac {1}{2}\) {ab – bc} = 0

{ab – bc} = 0

a = c