Answer to Question #294303 in Analytic Geometry for Nat

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

Given: A(-2,5), B(6,1) and C(-2,-3)

Mid point of AC = $(\frac {x_1+x_2}{2}, \frac{y_1+y_2}{2})=(\frac{-2+6}{2}, \frac{5+1}{2})=(2, 3)$

Let D be the mid point of AC so coordinate of D is (2,3).

Now, length of median from B to AC is BD.

B(6,1), D(2,3)

$BD=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(6-2)^2+(1-3)^2}=\sqrt{16+4}=2\sqrt{5}\ \text{unit}$