Question

If $A(2,2)$, $B(-4,-4)$ and $C(5,-8)$ are the vertices of a triangle, then the length of the median through vertex C is ___________.

• A. $\sqrt{65}units$
• B. $\sqrt{117}units$
• C. $\sqrt{85}units$
• D. $\sqrt{113}units$

Answer 1

Answer: (C)

$\sqrt{85}units$

Given the vertices of $△$ABC

i.e, $A(2,2),B(-4,-4)$ and $C(5,-8)$

The coordinates of mid-point of $AB$,

i.e,$D=(\frac{-4+2}{2},\frac{-4+2}{2})=(-1,-1)$

hence the length of medium through vertex $C=CD$

$=\sqrt{(5+1{)}^2+(-8+1{)}^2}=\sqrt{6^2+7^2}=\sqrt{85}$