Question

Triangle 2004-06-02-01-00_files/i0310000.jpg has vertices of A(–6, 7), B(4, –1), and C(–2, –9). Find the length of the median from 2004-06-02-01-00_files/i0310001.jpg in triangle 2004-06-02-01-00_files/i0310002.jpg.

Answer 1

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Answer 2

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Answer 3

I hope the equations (eqns.) of the medians are required.
I will work out the equation of the median AD through the vertex A(-6,7), where, D is the mid-point of the side BC.
We have, B=B(4,-1) and C(-2,-9).
Clearly, D=D((4-2)/2,(-1-9)/2)=D(1,-5).
Having A(-6,7) and D(1,-5), the slope of AD is {7-(-5)}/(-6-1)=-12/7.
Using the slope-point form eqn. of line, we get, the following eqn. of the median AD :
y-7=-12/7(x-(-6)), i.e., 7y-49=-12x-72, or, 12x+7y+23=0.
The other eqns. of the medians through the vertices B and C can be found similarly.
Enjoy Maths.!