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)

$25\sqrt{2}$

Answer 2

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 $MQ=\sqrt{{{(13+12)}^{2}}+{{(15+10)}^{2}}}$
$\sqrt{{{(25)}^{2}}+{{(25)}^{2}}}$ $\sqrt{2\times {{(25)}^{2}}}$
$=25\sqrt{2}$