Find the relation between x and y such that the point (x, y) is equidistant from (6, 2) and (4, 6).

Correct option is D

Given:
Point A = (6, 2)
Point B = (4, 6)
Point (x, y) is equidistant from both A and B
Concept Used:
A point is equidistant from two given points if its distance from each of those two points is the same.
Formula Used:
Distance between two point = $$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$​​
Solution:
Distance from (x, y) to (6, 2) = $$\sqrt{(x - 6)^2 + (y - 2)^2} \\$$​
Distance from (x, y) to (4, 6) $$= \sqrt{(x - 4)^2 + (y - 6)^2} \\$$​
As distance are equal from both points:
​$$(x - 6)^2 + (y - 2)^2 = (x - 4)^2 + (y - 6)^2 \\x^2 - 12x + 36 + y^2 - 4y + 4 = x^2 - 8x + 16 + y^2 - 12y + 36 \\-12x - 4y + 40 = -8x - 12y + 52 \\-4x + 8y - 12 = 0 \\-x + 2y - 3 = 0 \\\Rightarrow x - 2y = 3$$​​