Question

IF THE POINTS P(X,Y) IS EQUIDISTANT FROM THE POINTS A(5,1) AND B(1,5) THEN PROVE THAT X=Y

Answer 1

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Answer 2

Answer:

It is proven that $X=Y$ in the answer below.

Step-by-step explanation:

The given points are $A(5,1)$ and $B(1,5)$ and also it is given that,

The point $P(X,Y)$ is equidistant from the given points and we are required to prove that

$X=Y$

The distance between P and A is

$PA=\sqrt{(5-X)^2+(1-Y)^2$

The distance between P and B is

$PB=\sqrt{(1-X)^2+(5-Y)^2$

As both are equal we have,

$PA=PB= > PA^2=PB^2\\= > (5-X)^2+(1-Y)^2=(1-X)^2+(5-Y)^{2}\\= > X^2+Y^2-10X-2Y+26=X^2+Y^2-2X-10Y+26\\= > -10X-2Y=-2X-10Y= > -8X+8Y=0\\= > X=Y$

Hence it is proven that $X=Y$

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