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Question

Using the concept of slope, prove that medians of an equilateral triangle are perpendicular to the corresponding sides.

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Solution

Let each side be a
then BD=DC=a2
(AD is median to BC)
We have altitude of equilateral ABC=32a
(If AD is also an altitude apart from being median)
Also AD=AC2DC2=a2a24
=3a24=32a
Median of equilateral is also its altitude.

1204064_1201123_ans_82e16c9f992841a0b29522af936ebb5d.JPG

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