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Question
(–5, 2), (3, −6) and (7, 4) are the vertices of a triangle. Find the length of its median through the vertex (3, −6).
Solution
Let A(–5, 2), B(3, −6) and C(7, 4) be the vertices of the given triangle.
Let AD be the median through A, BE be the median through B and CF be the median through C.
We know that median of a triangle bisects the opposite side.
Co-ordinates of point F are
`((-5 + 3)/2, (2 - 6)/2) = ((-2)/2, (-4)/2) = (-1, -2)`
Co-ordinates of point D are
`((3 + 7)/2, (-6 + 4)/2) = (10/2, (-2)/2) = (5, -1)`
Co-ordinates of point E are
`((-5 + 7)/2, (2 + 4)/2) = (2/2, 6/2) = (1, 3)`
The median of the triangle through the vertex B(3, −6) is BE
Using distance formula,
`BE = sqrt((1 - 3)^2 + (3 + 6)^2)`
`BE = sqrt(4 + 81)`
`BE = sqrt(85)`
BE = 9.22
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