Question

Mid-points of the sides $AB$ and $AC$ of a $△ABC$ are $(3,5)$ and $(-3,-3)$ respectively, which of the following is the length of the side $BC$?

• A. $10units$
• B. $15units$
• C. $20units$
• D. $30units$

Answer 1

Answer: (C)

$20units$

R.E.F image

consider $\Delta ADE$ & $\Delta ABC$

As $\frac{AD}{AB}=\frac{AE}{AC};\angle ADE=\angle ABC=\theta$

$\angle BAC=$ Common

$\angle AED=\angle ACB=\varphi$

$\therefore \Delta ADE$ & $\Delta ABC$ are similar triangles

$\Rightarrow \frac{AD}{AB}=\frac{AE}{AC}=\frac{DE}{BC}=\frac{1}{2}\Rightarrow BC=2DE$

$DE=\sqrt{\left[\right(5-(-3){]}^2+[3-(-3){]}^2}=10\Rightarrow BC=20units$