If the point P(x,y) is equidistant from the points A(5,1) and B(1,5) p

1.	If the point P(x,y) is equidistant from the points A(5,1) and B(1,5) prove that x=y.
Answer» \xa0Given that PA = PB\xa0√(x- 5)2\xa0+ (y-1)2\xa0= √(x-1)2\xa0+ (y-5)2√x2\xa0-10x+25 +y2\xa0+1-2y = √ x2\xa0+1-2x+y2\xa0+25-10y√ x2\xa0-10x+y2-2y +26 = √ x2-2x+y2\xa0-10y +26squaring both sides, we getx2-10x +y2-2y +26= x2-2x+y2-10y +26-10x+2x = -10y+2y-8x = -8yx= y\xa0

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