Question

Find the length of the median through $(-2,-5)$ of the triangle whose vertices are $(-6,2),(2,-2),$ and $(-2,-5).$

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is C $5$

Let $A(-6,-2)B(2,-2)$ and $c(-2,-5)$ be the vertices of $△ABC$.

We have to find the median passing through $(-2,-5)$ so, it will also pass through the midpoint of $AB$ as we are concerned with the median.

$\text{midpoint}\left(AB\right)=(\frac{-6+2}{2},\frac{2-2}{2})$

$=(-2,0)$

So, from the above diagram we can say that length of $PC$ is the required median length,

$\begin{array}{cc}PC& =\sqrt{{(-2-(-2\left)\right)}^2+{(-5-0)}^2}\\ & =\sqrt{0+25}\\ & =5\text{units}\end{array}$