Question

Point P(x,y) is equidistant from the points A(-2,0) and B(3,-4). Prove that : 10x – 8y = 21

Answer 1

Step-by-step explanation:

Given, P(x,y),A(5,1),B(1,5)

Given, PA=PB (equidistant)

So by distance formula we have,

Distance between two points =

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

PA

2

=PB

2

⇒(x−5)

2

+(y−1)

2

=(x−1)

2

+(y−5)

2

⇒x

2

+25−10x+y

2

+1−2y+1−2y=x

2

+1−2x+y+25−10y

⇒−10x−2y+26=−2x−10y+26

⇒−5x−y=−x−5y

⇒4x=4y

⇒x=y (proved)