Question

if the point p(x, y) is equidistant from the point A(5,1)and(1,5),prove x=y​

Answer 1

Using distance formula, distance b/w points (x₁, y₁) , (x₂, y₂) is given by √(x₁ - x₂)² + (y₁ - y₂)².  In the question:

⇒ √(x - 1)² + (y - 5)² = √(x - 5)² + (y - 1)²

⇒ (x² + 1 - 2x) + (y² + 25 - 10y) = (x² + 25 - 10x) + (y² + 1 - 2y)

⇒ -2x - 10y = -10x - 2y

⇒ 10x - 2x = 10y - 2y

⇒ 8x = 8y

⇒ x = y                 proved