If p(x,y) is a point equidistance from the points A(6,-1)and B(2,3)sho

1.	If p(x,y) is a point equidistance from the points A(6,-1)and B(2,3)shoe thatx-y=3
Answer» Let A(6, -1) and B(2,3) be the given point and P(x,y) be the required point.Since point P is equidistant from points A and B,therefore,PA = PB\xa0{tex}\\Rightarrow{/tex}\xa0(PA)2\xa0= (PB)2{tex}\\Rightarrow{/tex}(x - 6)2\xa0+ (y + 1)2\xa0= (2 - x)2\xa0+ (3 - y)2{tex}\\Rightarrow{/tex}\xa036 + x2 - 12x + y2 + 1 +2y = 4 + x2 - 4x + 9 + y2 - 6y{tex}\\Rightarrow{/tex}\xa0-12x + 4x + 2y + 6y = 4 + 9 - 1 - 36{tex}\\Rightarrow{/tex}\xa0-8x + 8y = -24-8 (x - y)=-24{tex}\\Rightarrow{/tex}\xa0x - y = 3Hence, x - y = 3

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