The centre of a square of side 4 units length is (3,7) and one of the diagonals is parallel to the line y=x . If ( x ₁, y ₁ ), ( x ₂, y ₂ ), ( x ₃, y ₃ ) and ( x ₄, y ₄ ) are the vertices of this square, then y₁ y₂ y₃ y₄ x₁ x₂ x₃ x₄ =

Step-by-step solution

aligned & = (3 2 2 4 , 7 2 2 4 )=(3 2,7 2) & =(5,9) and (1,5) aligned (ii) Coordinates of D, B: aligned & (3 2 2 3 4 , 7 2 2 3 4 ) & =(3 2,7 2) & =(1,9) and (5,5) aligned So, we have: aligned & A (x₁, y₁ )=(1,5) and B (x₂, y₂ )=(5,5) & C (x₃, y₃ )=(5,9) and D (x₄, y₄ )=(1,9) aligned Now, y₁ y₂ y₃ y₄ x₁ x₂ x₃ x₄ = 5 5 9 9 1 5 5 1 =81