Question

A(2,4) B(0,0,) C(4,2) are the vertices of a triangle find the length of the median drown from the vertex a to opposite side of the triangle​

Answer 1

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

$\textsf{Vertices of triangle ABC are}$

$\mathsf{A(2,4),\;B(0,0),\;C(4,2)}$

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

$\textsf{Length of the median from A to the opposite side}$

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

$\textsf{First we find midpoint of side BC}$

$\mathsf{Midpoint\;of\;BC=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}$

$\mathsf{Midpoint\;of\;BC=\left(\dfrac{0+4}{2},\dfrac{0+2}{2}\right)}$

$\mathsf{Midpoint\;of\;BC=\left(\dfrac{4}{2},\dfrac{2}{2}\right)}$

$\mathsf{Midpoint\;of\;BC=(2,1)}$

$\underline{\textsf{Length of the median from A}}$

$\textsf{=Distance between A and midpoint of BC}$

$\mathsf{=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}}$

$\mathsf{=\sqrt{(0-2)^2+(0-1)^2}}$

$\mathsf{=\sqrt{4+1}}$

$\mathsf{=\sqrt{5}}$

$\underline{\textbf{Find more:}}$