Question

Show that the points (1, 7), (4, 2), (-1, -1) and (-4, 4) are the vertices of a square.

Answer 1

Let A(1, 7), B(4, 2), C(-1, -1) and D(-4, 4) be the given points. 

To prove that ABCD is a square, 

We have to prove that all its sides are equal and both its diagonals are equal.

Since, AB = BC = CD = DA and AC = BD, all the four sides of the quadrilateral ABCD are equal and its diagonals AC and BD are also equal. 

Therefore, ABCD is a square.