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

show that the points (1 ,7) (4, 2) (-1, -1) and(-4 ,4 )are the vertice

1.	show that the points (1 ,7) (4, 2) (-1, -1) and(-4 ,4 )are the vertices of a square
Answer» Let the given vertices be A (1,7), B (4,2), C (-1,-1), D (-4,4)AB = √ (4-1)2 + (2 -7)2 = √ 9 + 25 = √ 34BC = √ (-1-4)2 + (-1-2)2 = √ 25 + 9 = √ 34CD = √ (-4+1)2 + (4 +1)2 = √ 9 + 25 = √ 34AD = √ (1 +4)2 + (7 -4)2 = √ 25 + 9 = √ 34AC = √ (-1-1)2 + (-1-7)2 = √ 4 + 64 = √ 68BD = √ (-4-4)2 + (4 - 2)2 = √ 64 + 4 = √ 68Clearly, AB = BC = CD = DA and AC = BDHence, given points are the vertices of a square