Question

Find the value of p for which the points A(–5, 1), B(1, p) and C(4, –2) are collinear.

Answer 1

Given: A(–5, 1), B(1, p) and C(4, –2).

Step-wise calculation:

1. Slope AB = `(p - 1)/(1 - (-5))`

= `(p - 1)/6`

2. Slope AC = `(-2 - 1)/(4 - (-5))`

= `(-3)/9`

= `-1/3`

3. For collinearity slopes must be equal:

`(p - 1)/6 = -1/3`

4. Multiply both sides by 6:

p – 1 = –2

⇒ p = –1

The three points are collinear when p = –1.