Given points
A(2,−2),B(8,4),C(5,7) and D(−1,1)
AC=√(2−5)2+(−2−7)2=√90
BD=√(8−(−1))2+(4−1)2=√90
⇒ Diagonals AC and BD are equal. (property of rectangle)
AB=√(2−8)2+(−2−4)2=√72
CD=√(5−(−1))2+(7−1)2=√72
AB=CD
Similarly by distance formula
BC=AD
⇒ AB=CD & BC=AD and diagonals are also equal.
⇒ ABCD is a rectangle