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} $