Question

If $P(2,2),Q(-2,4)$ and $R(3,4)$ are the vertices of $\Delta PQR$ then the equation of the median through vertex R is _______.

• A. $x+3y=9=0$
• B. $x-3y+9=0$
• C. $x-3y-9=0$
• D. $x+3y-9=0$

Answer 1

The correct option is B $x-3y+9=0$

The median through vertex R passes through R and the midpoint of its opposite side PQ,

Midpoint of PQ = ($\frac{2-2}{2},\frac{2+4}{2}$)=($0,3$) and $R=(3,4)$

So, Slope of median = $\frac{4-3}{3-0}=\frac{1}{3}$

Thus equation of median is $y-4=\frac{1}{3}(x-3)\to x-3y+9=0$