Question

The point $(22,33)$ divides the join of $P(7,5)$ and $Q$ externally in the ratio $3:5$, then coordinates of $Q$ are

• A. $(3,7)$
• B. $(-3,-7)$
• C. $(3,-7)$
• D. $(-3,\frac{-41}{3})$

Answer 1

The correct option is B $(-3,-7)$

Let the point $Q$ be $(x,y)$

As the point $(22,23)$ diverts the line joining point $P(7,5)$ and $Q(x,y)$ in $3:5$ externally.

So.

$22=\frac{3\left(x\right)-5\left(7\right)}{3-5}23=\frac{3\left(y\right)-5\left(5\right)}{3-5}$

$22=\frac{3x-35}{-2}23=\frac{3y-25}{-2}$

$-44=3x-35-46=3y-25$

$-=3x-21=3y$

$x=-3y=\frac{-21}{3}=-7$

Point $Q=(-3,-7)$