Question

Let $A$ and $B$ be points $(8,10)$ and $(18,20),$ respectively. If the point $Q$ divides AB externally in the ratio $2:3$ and $M$ is the $S$ mid-point of $AB$, then the length $MQ$ is equal to

• A. $25$
• B. $5\sqrt{34}$
• C. $25\sqrt{2}$
• D. $5\sqrt{26}$

Answer 1

Answer: (C)

Given points are $A(8,10)$ and $B(18,20)$ . M is the mid-point of AB. Coordinates of $M=\left(\frac{8+18}{2}.\frac{10+20}{2}\right)=(13,15)$ Point Q divides AB externally in the ration of $2:3$ Day The coordinates of Q
$=\left(\frac{2\times 18-3\times 8}{2-3},\frac{2\times 20-3\times 10}{2-3}\right)$
$=\left(\frac{36-24}{-1},\frac{40-30}{-1}\right)$
$=(-12,-10)$
Now, length $MQ=\sqrt{{(13+12)}^2+{(15+10)}^2}$
$\sqrt{{(25)}^2+{(25)}^2}$ $\sqrt{2\times {(25)}^2}$
$=25\sqrt{2}$