Question

Plot the following point and verify if it is collinear.

A(−1, 2), B(3, −1) and C(7, −4)

Answer 1

For Collinearity   

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]

Area = `1/2 |− 1((− 1) − (−4) + 3 (( − 4) − 2) + 7(2 − (− 1))|`

Area = `1/2 | − 1 (3) + 3(− 6) + 7(3)|`

= `1/2 xx 0`

= 0

Slope of AB = `(− 1 − 2)/(3 − (−1)) = −3/4`

Slope of BC = `(− 4 − (−1))/(7 − 3)`

= `(− 3)/4`

If the area = 0, the points are collinear.

Yes, the points A, B, and C are collinear.