Answer to Question #194968 in Analytic Geometry for Paulina

Question #194968

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) 


1
Expert's answer
2021-05-19T08:05:44-0400

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) = x1+x22\dfrac{x1 + x2}{2} , y1+y22\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 = (15)2+(37)2\sqrt{(1-5)^2 + (-3 - 7)^2}


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


AP = 116\sqrt{116}

AP = 10.7 units.


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