Question

$P(-7,1),Q(x,4)$ and $R(3,y)$ are collinear and $PQ=QR.$ Find the values of $x$ and $y.$

Answer 1

$P(-7,1)$ $Q(x,4)$ $R(3,4)$ are collinear

$\Rightarrow$ These points are in a line

since, $PQ=QR$

$\Rightarrow Q$ divides line $PR$ in $1:1$

$\Rightarrow Q$ is the mid point of $PR$

mid point of PR $=$ Point $Q$

$\Rightarrow (\frac{-7+3}{2},\frac{y+1}{2})=(x,4)$

comparing the co-ordinates

$\Rightarrow \frac{-4}{2}=x,$ $\frac{y+1}{2}=4$

$\Rightarrow x=-2$ $y+1=8$

$y=7$

$\Rightarrow x=-2\&y=7$

Hence, the answer is $-2,7.$