Question

The coordinates of the vertices of a triangle ABC are A(2, 4), B(5, 1), C(-1, -1). find the equation of the median drawn from vertex A ​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Vertices of triangle ABC are}$

$\textsf{A(2, 4), B(5, 1), C(-1, -1)}$

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

$\textsf{The equation of median drawn from vertex A}$

$\underline{\textsf{Solution:}}$

$\textsf{Median from A is a line segment joining A and the midpoint}$

$\textsf{of the side BC}$

$\textsf{Midpoint of side BC}$

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

$\mathsf{(\dfrac{5+(-1)}{2},\dfrac{1+(-1)}{2})}$

$\mathsf{(\dfrac{4}{2},\dfrac{0}{2})}$

$\mathsf{(2,0)}$

$\textsf{Now}$

$\textsf{The equation of median drawn from A}$

$\textsf{is the equation of the line joining (2,4) and (2,0)}$

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

$\mathsf{\dfrac{y-4}{0-4}=\dfrac{x-2}{2-2}}$

$\mathsf{\dfrac{y-4}{-4}=\dfrac{x-2}{0}}$

$\implies\boxed{\mathsf{x-2=0}}$

$\underline{\textsf{Answer:}}$

$\textsf{The equation of the median drawn from A is x-2=0}$