#### Question

If the distances of P(*x, y*) from A(5, 1) and B(–1, 5) are equal, then prove that 3*x* = 2*y*

#### Solution

Given: PA = PB

To Prove: 3x = 2y

Proof: Since PA = PB

So, according to the distance formula,

`=> sqrt((x-5)^2 + (y - 1)^2) = sqrt((x+1)^2 + (y - 5)^2)`

⇒(x−5)^{2 }+ (y−1)^{2 }= (x+1)^{2 }+(y−5)^{2} (Squaring both sides)

⇒x^{2 }− 10x + 25 + y^{2} − 2y + 1 = x^{2} + 2x + 1 + y^{2} − 10y +25

⇒−10x − 2y = 2x − 10y

⇒8y = 12x

⇒3x = 2y

Hence, 3x = 2y.

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Solution If the Distances of P(X, Y) from A(5, 1) and B(–1, 5) Are Equal, Then Prove that 3x = 2y Concept: Distance Formula.