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Question

Find the lengths of the medians AD and BE of ABC whose vertices are A(7, −3), B(5, 3) and C(3, −1). [CBSE 2014]

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Solution

The given vertices are A(7, −3), B(5, 3) and C(3, −1).
Since D and E are the midpoints of BC and AC respectively, therefore
Coordinates of D=5+32, 3-12=4, 1Coordinates of E=7+32, -3-12=5, -2
Now
AD=7-42+-3-12=9+16=5BE=5-52+3+22=0+25=5
Hence, AD = BE = 5 units.

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