Question

Prove that P(−2, 2), Q(1, 4) and R(7, 8) are collinear.

Answer 1

Step 1: Use the Area of Triangle Formula

P(x₁, y₁) = (−2, 2)

Q(x₂, y₂) = (1, 4)

R(x₃, y₃) = (7, 8)

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]

= `1/2|(−2)(4 − 8) + 1(8 − 2) + 7(2 − 4)|`

= `1/2 |8 + 6 − 14|`

= `1/2|0|`

= 0

Area = 0 the points P(−2, 2), Q(1, 4), and R(7, 8) are collinear.