Question

P(2,3),Q(7,-2) and R(-2,-1) are the vertices of triangle PQR. Write down the equation of the median of triangle through R​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Vertices of triangle PQR are}$

$\textsf{P(2,3), Q(7,-2), R(-2,-1)}$

$\underline{\textbf{To find:}}$

$\textsf{Median of triangle through R}$

$\underline{\textbf{Solution:}}$

$\textsf{Mid point of P and Q}$

$\mathsf{\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}$

$\mathsf{\left(\dfrac{2+7}{2},\dfrac{3-2}{2}\right)}$

$\mathsf{\left(\dfrac{9}{2},\dfrac{1}{2}\right)}$

$\textbf{Equation of median through R}$

$\textsf{=Equation of line joining Mid point of PQ and R}$

$\implies\mathsf{\dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}}$

$\implies\mathsf{\dfrac{y-\dfrac{1}{2}}{-1-\dfrac{1}{2}}=\dfrac{x-\dfrac{9}{2}}{-2-\dfrac{9}{2}}}$

$\implies\mathsf{\dfrac{\dfrac{2y-1}{2}}{\dfrac{-3}{2}}=\dfrac{\dfrac{2x-9}{2}}{\dfrac{-13}{2}}}$

$\implies\mathsf{\dfrac{2y-1}{-3}=\dfrac{2x-9}{-13}}$

$\implies\mathsf{-13(2y-1)=-3(2x-9)}$

$\implies\mathsf{-26y+13=-6x+27}$

$\implies\mathsf{6x-26y+13-27=0}$

$\implies\mathsf{6x-26y-14=0}$

$\implies\boxed{\mathsf{3x-13y-7=0}}$

$\underline{\textbf{Formula used:}}$

$\boxed{\begin{minipage}{7cm} \\\mathsf{Equation\;of\;line\;joining\;(x_1,y_1)\;and\;(x_2,y_2)\;is}\\\\\mathsf{\dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}}\\ \end{minipage}}$