Question

If the points (x,y) is equidistant from the points (m+n,n-m) and (n+m , m+n) Find N.

Answer 1

Given :   points (x,y) is equidistant from the points (m+n,n-m) and (n+m , m+n)

To find :  n

Solution:

points (x,y) is equidistant from the points (m+n,n-m) and (n+m , m+n)

=> ( m + n - x)²  + ( n -  m - y)²  = (n + m - x)² +  (m + n - y)²

=>  ( m + n - x)²  + ( (n  - y) - m)²  = (m + n - x)² + ( (n  - y) + m)²

Cancelling  ( m + n - x)²  from both sides

=> ( (n  - y) - m)²  =   ( (n  - y) + m)²

=>   (n  - y)² + m²  - 2m(n-y)  =  (n  - y)² + m²  + 2m(n-y)

cancelling (n  - y)² + m²  from both sides

=>  - 2m(n-y)  =   + 2m(n-y)

Dividing by 2m on both sides

=>  -(n- y) = n - y

=> - n + y =  n - y

=> 2n  = 2y

=> n = y

n = y

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