if twoopposite vertices of a square are (1,-6) and (5,4) . Find the coordinates of two other vertices ?

Let ABCD be a square and let A (1, -6) and C (5, 4) be the given points.

Let B(x₁, y₁) and D B(x₂, y₂) is the unknown vertex.

Since, square have equal sides,

Therefore,

In triangle ABC, we have,

Substituting the value of x1 from equation (1) into equation (2), we get,

Substitute values of y1 in equation (1), we get,

Hence, other two vertices are B (8, -3) and D (-2, 1).