Question

find the relation between x And y such that the point (x,y) is equidistant from the points (7,1) ,( 3,5)​

Answer 1

Answer:

        x - y - 2 = 0

Step-by-step explanation:

    Distance from (x,y) to (7,1)  =  distance from (x,y) to (3,5)

⇒  Square of distance (x,y) to (7,1)  =  square of distance (x,y) to (3,5)

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

⇒  [ (x-7)² - (x-3)²) ] + [ (y-1)² - (y-5)² ]  =  0

    ( now use difference of squares a² - b² = (a-b)(a+b) )

⇒  [ (x-7) - (x-3) ] [ (x-7) + (x-3) ]  +  [ (y-1) - (y-5) ] [ (y-1) + (y-5) ]  =  0

⇒  [ -4 ] [ 2x - 10 ]  +  [ 4 ] [ 2y - 6 ]  =  0

⇒  -2x + 10 + 2y - 6  =  0

⇒  -x + y + 2 = 0    or equivalently   x - y - 2 = 0.