Question

The line segment joining a vertex of a triangle and the midpoint of the opposite side is called the median of the triangle. Given a triangle whose vertices are A(4,-4), B(10, 4) and C(2, 6), find the point on each median that is two-thirds of the distance from the vertex to the midpoint of the opposite side.

Answer 1

Since all three medians meet there, finding where two intersect is enough.

AB has midpoint P at (5,0)
BC has midpoint Q at (6,5)

The lines CP and AQ are
y-6 = (0-6)/(5-2) (x-2)
y+4 = (5+4)/(6-4) (x-4)

Now just find where the two lines intersect.

Answer 2

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Answer 3

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Answer 4

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