# If the Points P (X , Y) is Point Equidistant from the Points a (5,1)And B ( -1,5) , Prove that 3x=2y - Mathematics

If the points p (x , y) is point equidistant from the points A (5,1)and B ( -1,5) , Prove that 3x=2y

#### Solution

As per the question, we have

AP = BP

⇒ 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.

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 11