Is the point p(x,y) is equidistant pointA(5,1)B(_-1,5)prove that 3x=2y

1.	Is the point p(x,y) is equidistant pointA(5,1)B(_-1,5)prove that 3x=2y
Answer» \xa0The distances of P (x, y) from A (5,1) and B (-1,5) are equal, then we have to prove that 3x = 2y.PA = PB{tex}\\therefore{/tex}\xa0PA2\xa0= PB2By distance formula,(5 - x)2\xa0+ (1 - y)2= (-1 - x)2\xa0+ (5 - y)2{tex}\\Rightarrow{/tex}25 - 10x + x2\xa0+ 1 - 2y + y2\xa0= 1 + 2x + x2\xa0+ 25 - 10y + y2{tex}\\Rightarrow{/tex}\xa0-10x - 2y = 2x - 10y{tex}\\Rightarrow{/tex}\xa08y = 12x{tex}\\Rightarrow{/tex}4(2y)= 4(3x){tex}\\Rightarrow{/tex}3x = 2yHence Proved.

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