Question

If the points A, B, C is collinear then the area of the triangle will be zero.

(a) True

(b) False

I got this question in class test.

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

Answer 1

Right choice is (b) False

The best I can explain: We know that, area of triangle = \(\frac {1}{2}\){x1 (y2 – y3 ) + x2 (y3 – y1 ) + x3 (y1 – y2 )}

Let us assume the vertices of the triangle are (0, 0), (0, 4) and (0, 9).

The area of triangle = \(\frac {1}{2}\) {0(4 – 9) + 0(9 – 0) + 0(0 – 4) } = \(\frac {1}{2}\){0} = 0 units

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