Question

which of the following points is an equal distance (equidistant) from a(2, −2) and b(−4, 6)?

Answer 1

The point equidistant from a(2, -2) and b(-4, 6)  is the midpoint

For (x₁, y₁) and (x₂, y₂) the midpoint is given by:

 ( (x₁ + x₂)/2 ,  (y₁ + y₂)/2 )

Midpoint = ( (2 + -4)/2 , (-2 + 6)/2 )

               =  ( (2 - 4)/2 ,  (6 - 2)/2) ) = ( -2/2,  4/2) = (-1,  2)

So the point equidistant from the two points is (-1, 2).