Question

If the point $A(-2,1),B(a,b)$ and $C(4,-1)$ are collinear of $a-b=1$. Find the value of $a$ of $b$.

Answer 1

Given that points $(-2,1),(a,b)$ and $(4,-1)$ are collinear.

Using the point-slope formula,

$\frac{b-1}{a-(-2)}=\frac{-1-1}{4-(-2)}$

$\Rightarrow \frac{b-1}{a+2}=\frac{-1}{3}$

$\therefore 3b-3=-a-2$

$a+3b=1$

Also,

Given that $a-b=1$

Using both the equations, we get

$a=1,b=0$