Question

P(3, 4), Q(7, -2) and R(-2, -1) are the vertices of a triangle PQR. Find the equation of the median of the triangle through R.

• A. 2x-7y-3=0
• B. 7x-2y-3=0
• C. 2x-7y-5=0
• D. 3x-8y-5=0

Answer 1

The correct option is A

2x-7y-3=0

The vertices of $\Delta PQR$ are P(3, 4), Q(7, -2) and R(-2, -1)
Let S be the mid-point of PQ, $\Rightarrow$ RS is the median through R

$\therefore$ Coordinates of S are
$(\frac{3+7}{2},\frac{4-2}{2})=(5,1)$
Slope of RS, $m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-1)}{5-(-2)}=\frac{2}{7}$
$\therefore$ The equation of the median RS is
$y-y_1=m(x-x_1)$
$\Rightarrow y-(-1)=\frac{2}{7}(x+2)$
$\Rightarrow y+1=\frac{2}{7}(x+2)$
$\Rightarrow 7y+7=2x+4$
$\Rightarrow 2x-7y-3=0$
Hence, the equation of the median of the triangle through R is $2x-7y-3=0$