Answer to Question #290867 in Analytic Geometry for Kat

Question

In the triangle ABC having vertices at A(-2,5), B(6,1) and C(-2,-3) , find the length of the median from vertex B to side AC .

Answer 1

Find the coordinates of the point E - the midpoint of AC:

$E\left( {\frac{{ - 2 - 2}}{2};\frac{{5 - 3}}{2}} \right) \Rightarrow E\left( { - 2;\,1} \right)$

Thenthe length of the median is

$BE = \sqrt {{{\left( { - 2 - 6} \right)}^2} + {{\left( {1 - 1} \right)}^2}} = 8$

Answer: 8