Question

Find the values of p for which the points $(-5,1),(1,p)$ and $(4,-2)$ are collinear.

Answer 1

$x₁=-5$

$x₂=1$

$x₃=4$

$y₁=1$

$y₂=p$

$y₃=-2$

For the points to be collinear $:-$

$x₁(y₂-y₃)+x₂(y₃-y₂)+x₃(y₁-y₂)=0$

$-5p-(-2)+1(-2-1)+4(1-p)=0$

$-5(p+2)+1(-3)+4(1-p)=0$

$-5p-10-3+4-4p=0$

$-9p-9=0$

$-9p=9$

$p=9/-9$

$p=-1$