Question

Plot the following point and verify if it is collinear.

M(−2, 5), N(4, 2) and P(8, 0)

Answer 1

Slope Method

Find slope of MN

`m_(MN)`,

= `(2 − 5)/(4 − (−2))`

= `(− 3)/6`

= ` − 1/2`

Find slope of NP

`m_(NP)`,

= `(0 − 2)/(8 − 4)`

= `(− 2)/4`

= `− 1/2`

Compare slopes

`m_(MN)`​ = `m_(NP)` ​

= `1/2`

Points M, N, and P are collinear

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]

M = (x1,y1) = (−2, 5)

N = (x2, y2) = (4, 2)

P = (x3, y3) = (8, 0)

Area = `1/2|−2(2 − 0) + 4(0 − 5) + 8(5 − 2)|`

Area = `1/2| − 4 − 20 + 24|`

Area = `1/2(0)`

Area = 0

Area is zero, and All three points M(−2, 5), N(4, 2) and P(8, 0) so the points are collinear.