Question

if point (x,y) is equidistant from point ( 7,1 ) and (3,5) ,show that y= x-2

Answer 1

Hey friend,

Please refer the attachment for your answer.

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Answer 2

Answer:

The proof is given below

Step-by-step explanation:

Given,

Point (x,y) is equidistant from point ( 7 , 1 ) and ( 3 , 5 )

By distance formula we know,

d = √( x₂ - x₁ )² + ( y₂ - y₁ )²

Distance of ( x , y ) from ( 7 , 1 )

Substituting the values in the distance formula,

d = √( x - 7 )² + ( y - 1 )²

Distance of ( x , y ) from ( 3 ,5 )

Substituting the values in the distance formula,

d = √( x - 3 )² + ( y - 5 )²

Since point ( x , y ) is equidistant from both the points,

Both the distances will be equal

Therefore,

√( x - 7 )² + ( y - 1 )²  = √( x - 3 )² + ( y - 5 )²

Squaring both the sides,

( x - 7 )² + ( y - 1 )² = ( x - 3 )² + ( y - 5 )²

x² + 49 - 14x + y² + 1 - 2y = x² + 9 - 6x + y² + 25 - 10y

x² - x² + y²- y² - 14x + 6x - 2y + 10y + 49 + 1 - 9 - 25 = 0

- 8x + 8y + 16 = 0

Dividing the entire equation by 8

- x + y + 2 = 0

y = x -2

Hence proved