Q) Point P(x, y) is equidistant from points A(5, 1) and B(1,5). Prove that x = y.
Ans: Let’s draw the diagram to solve:
Given that PAĀ = PB
Hence, PA2Ā = PB2
Ā Ā (x – 5)2Ā + (y – 1)2 = (x – 1)2 + (y – 5)2
– 10 x – 2y = – 2 x – 10 y
– 8 x = – 8 y
x = y ……………………….Hence ProvedĀ
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Ā Ā (x – 5)2Ā + (y – 1)2 = (x – 1)2 + (y – 5)2