Question

Prove that A(7, 13), B(3, 9) and C(−6, 0) are collinear.

Answer 1

Step 1: Use the Area of Triangle Formula

A(x₁, y₁) = (7, 13)

B(x₂, y₂) = (3, 9)

C(x₃, y₃) = (−6, 0)

Area = `1/2 |x_1(y_2 − y3) + x_2(y_3 − y_1) + x_3(y_1 − y_2)|`   ... [use the area of triangle method]

Step 2: Substitute the coordinates

`1/2|7(9 − 0) + 3(0 − 13) + (−6) (13 − 9)|`

= `1/2|63 − 39 − 24|`

= `1/2|0|`

= 0

Since the area = 0, the points A(7, 13) B(3, 9) and C(−6, 0) are collinear.

Therefore, A, B and C are collinear.