Question

Determine whether the three points are collinear if
P((-1,4), Q(-2,-1), R(1,14)

Answer 1

see explanation

Explanation:

If the 3 points are collinear then the slope of PQ should equal the slope of QR

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = P(- 1, 4) and (x₂, y₂ ) = Q(- 2, - 1)

`m_(PQ)` =
`(-1-4)/(-2+1)` =
`(-5)/(-1)` = 5

Repeat using

(x₁, y₁ ) = Q(- 2, - 1) and (x₂, y₂ ) = R(1, 14)

`m_(QR)` =
`(14+1)/(1+2)` =
`(15)/(3)` = 5

Since the slopes of the 2 segments are equal then the 3 points are collinear.