Question

The co-ordinates of $A$ and $B$ are $(-3,\alpha )$ and $(1,\alpha +4)$ and the midpoint of $AB$ is $P(-1,1).$Find the value of $\alpha .$

Answer 1

$M$ is the midpoint of $AB$

Using midpoint formula,$P(-1,1)=(\frac{-3+1}{2},\frac{\alpha +\alpha +4}{2})$

$P(-1,1)=(\frac{-2}{2},\frac{2\alpha +4}{2})$

$P(-1,1)=(-1,\alpha +2)$

Comparing the $y-$ coordinates, we get

$\alpha +2=1$

$\Rightarrow \alpha =1-2=-1$

$\therefore \alpha =-1$