Question

Find the equation of the median of a triangle of the coordinates of which vertices are (-1,6),(-3,-9), and (5,4).

Answer 1

Given : coordinates of vertices of Triangle are (-1,6),(-3,-9), and (5,4).

To Find : equation of the median

Solution:

A  ( - 1 , 6)

B  ( - 3 , - 9)

C ( 5 , 4)  

A ( - 1 , 6)

D mid point of BC   B  ( - 3 , - 9)  C ( 5 , 4)  

B = (-3 + 5)/2 , ( - 9 + 4)/2  = ( 1 , - 5/2)  

A ( - 1 , 6) ,  D ( 1 , - 5/2)  

Slope of AD =  (-5/2 - 6)/(1 - (-1))

= -17/4

y - 6 = -17/4(x - (-1))

=> 4y - 24 = -17x - 17

=> 17x + 4y  = 7

Similarly find Equation of Median BE  & CF

E mid point of AC

F mid point of AB

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