(Q21)Show that the points (1,7) , (4,2) , (-1,-1) and (-4,4) are the vertices of the square.

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

On way of showing that ABCD is a square is to use property that all its sides should be equal and both its diagonals should also be equal.Now the sides are

AB = √(( - )2 + ( - )2) = √ units

BC = √(( + )2 + ( + )2) = √ units

CD= √((- + )2 + (- - )2) = √ units

DA = √((- - )2 + ( - )2) = √ units

and diagonal are

AC = √(( + )2 + ( + )2) = √ units

BD = √(( + )2 + ( - )2) = √ units

Since AB = BC = CD = DA and AC = BD. So all the four sides of the quadrilateral ABCD are equal and its diagonals AC and BD are also equal. Therefore ABCD as a square.