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If P(X , Y) is Point Equidistant from the Points A(6, -1) and B(2,3) a , Show that X – Y = 3 - Mathematics

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If  p(x , y)  is point equidistant from the points A(6, -1)  and B(2,3) A , show that x – y = 3

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Solution

The given points are A(6,-1) and B(2,3). The point P(x, y) equidistant from the points A and B So, PA = PB

Also,` (PA)^2 = (PB)^2`

`⇒ (6-x)^2 +(-1-y)^2 = (2-x) ^2 +(3-y)^2`

`⇒ x^2-12x +36+y^2+2y+1=x^2-4x+4+y^2-6y+9`

`⇒x^2 +y^2-12 x +2y +37 = x^2 -4x-6y+13`

`⇒ x^2 +y^2 -12x +2y -x^2 -y^2 +4x +6y = 13-37`

⇒ -8x +8y = -24

⇒-8 (x-y) = -24 

`⇒x-y =(-24)/(-8)`

`⇒ x-y = 3`

Hence proved

 

 

 

 

 

Concept: Coordinate Geometry
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 12

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