Question

prove that the points A(2,3) , B(-2,2).C(-1,-2) and D(3,-1) are the vertices of the square ABCD. also find the length of the diagonal.

Answer 1

length OF SIDES-
AB = √[(2+2)² +(3-2)² ]
= √[16+1]
= √17
BC = √[(-2+1)² + (2+2)²]
= √[1+16]
= √17
CD = √[(-1-3)² + (-2+1)²]
= √17
DA = √[(3-2)² +(-1-3)²]
= √17
here AB=BC=CD=DA

LENGTH OF DIAGONALS
AC = √[(2+1)² + (3+2)²]
= √[9+25]
= √34
BD = √[(-2-3)² + (2+1)²]
= √34
here AC=BD
hence, the given points are vertices of a square

Answer 2

Step-by-step explanation:

first find the lengths of sides

then lengths of diagonals

If all sides are equal and also both diagonals are equal then the points are vertices of a square