Question

Three vertices of a square are p (-1,-9), Q (3,-1), R(-5,3). Find the coordinates of vertex S.

Answer 1

Mid Point Formula

→ (x₁+ x₂)/2 , (y₁ + y₂)/2 = (Coordinate of mid point)

→ (- 1 - 5)/2, (- 9 + 3)/2 = LHS

→ - 3, - 3 = LHS

→ (3 + x)/2, (- 1 + y)/2 = RHS

Since, in a square diagnonals are equal and bisect each other.

→ (3 + x)/2, (-1 + y)/2 = - 3, - 3

→ (3 + x)/2 = - 3 and (-1 + y)/2 = - 3

→ 3 + x = - 6 and - 1 + y = - 6

→ x = - 9 and y = - 5

Hence, Coordinate of Vertex S is - 9, - 5.

Answer : (- 9, - 5)