Question

let us show that the points (2,-2),(8,4),(5,7) and (-1,1) are the vertices of rectangle.

Answer 1

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Answer 2

Hiii friend,


Let A(2,-2) , B(8,4) , C(5,7) and D(-1,1) be the vertices of Rectangle ABCD

Then,


A(2,-2) and B(8,4)


Here,


X1 = 2 , Y1 = -2 and X2 = 8 ,Y2 = 4

Using distance formula,


AB² = (X2-X1)² + (Y2-Y1)²

AB² = (8-2)² + (4-(-2)²

AB² = (6)² + (4+2)²

AB² = (36 + 36)

AB² = 72

Therefore,


AB = ✓72



B(8,4) and C(5,7)


Here,


X1 = 8 , Y1 = 4 and X2 = 5 , Y2 = 7


BC² = (X2-X1)² + (Y2-Y1)²

BC² = (5-8)² + (7-4)²


BC² = (-3)² + (3)²

BC² = 9 +9

BC² = 18

BC = ✓18 => 3✓2


C(5,7) and D(-1,1)


Here,


X1 = 5 , Y1 = 7 and X2 = -1 ,Y2 = 1


CD² = (X2-X1)² + (Y2-Y1)²


CD² = (-1-5)² + (1-7)²


CD² = (-6)² + (-6)²

CD² = 36 + 36


CD² = 72

CD = ✓72 units.

And,


A(2,-2) and D(-1,1)


Here,


X1 = 2 , Y1 = -2 and X2 = -1 , Y2 = 1


AD² = (X2-X1)² + (Y2-Y1)²

AD² = (-1-2)² + (1-(-2)²

AD² = (-3)² + (3)²


AD² = 9 +9

AD² = 18


AD = ✓18 = 3✓2 units


Thus,


AB = CD = ✓72 and BC = AD = 3✓2



Hence,


ABCD is a rectangle whose opposite sides are equal.




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