Question

The points A (3, 0), B (4, 5) and C (6, 7) are collinear.

(a) True

(b) False

The question was posed to me in examination.

This intriguing question comes from Geometry topic in division Coordinate Geometry of Mathematics – Class 10

Answer 1

The correct option is (b) False

Best explanation: 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 A (3, 0), B (4, 5) and C (6, 7)

The area of triangle = \(\frac {1}{2}\) {3(5 – 7) + 4(7 – 0) + 6(0 – 5)} = \(\frac {1}{2}\) {-8} = – 4 units

Since, the area of triangle is not zero.

Therefore, the points are not collinear.