Find all points on the of the form 2y which are 3 units from

Find all points on the of the form (2,-y) which are 3 units from the point (-1,2).

(A) (2,0)

(B) (2,-1)

(C) (2,-2)

(D) (2,2)

Solution

Distance between two points (x₁ , y₁) and (x₂ , y₂) is D = [(x₂ - x₁)² + (y₂ - y₁)²]

Given that Distance between two points (2 , -y) and (-1 , 2) is 3

==> 3 = [(-1 - 2)² + (2 - (-y))²]

==> 3 = [(-3)² + (2 + y)²]

==> squaring on both sides

==> 3² = 3² + (2 + y)²

==> (2 + y)² = 0

==> y = -2

Hence point is (2 , -y) = (2 , -(-2)) = (2 , 2)

Hence (2 , 2) is 3 units away from (-1 , 2)

Option D is correct