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Question

Prove that the co-ordinates of the third vertex of an equilateral triangle whose two vertices are at (3,4) and (2,3) are (1+32,7532) or (132,7+532)

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Solution

PA2=PB2=26=AB2
PA2=PB2 imply 5h+k=6
PA2=26 imply
(h3)2+(k4)2=26
Eliminate k between (1) and (2),
2h22h1=0
h=1+32 or 1+32
k=7532 or 7+532.

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