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in Coordinate Geometry by (49.2k points)
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If A (–1, 3), B (1, –1) and C (5, 1) are the vertices of triangle ABC, find the length of the median through A.

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Let AD be the median though A of ΔABC. 

Then, D is the mid-point of BC. 

Co-ordinates of D are \(\bigg(\frac{1+5}{2},{\frac{-1+1}{2}}\bigg), i.e, (3,0)\)

∴ AD = \(\sqrt{(3+1)^2+(0-3)^2}\)

\(\sqrt{16+9} = \sqrt{25}=5\) units.

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