Answer to Question #194968 in Analytic Geometry for Paulina

Question

What is the length of the median from point A in a triangle with the the vertices A(5, 7) * B * (7, - 5) and C(- 5, - 1) 

Answer 1

A (5, 7)

B (7, - 5)

C (- 5, - 1) 

Let the mid - point of BC be P(x, y)

By mid point formula we have

P(x, y) = $\dfrac{x1 + x2}{2}$ , $\dfrac{y1 + y2}{2}$

where x1 , y1 are the coordinates of B and x2, y2 are the coordinates of C .

P(x, y) = (1, -3)

Now the length the median from a can be found by calculating the distance between A and P

AP = $\sqrt{(1-5)^2 + (-3 - 7)^2}$

AP = $\sqrt{(-4)^2 + (-10)^2}$

AP = $\sqrt{116}$

AP = 10.7 units.