Question

What type of a quadrilateral do the points A(2,-2),B(7,3),C(11,-1)andD(6,-6)

taken in thatborder form?​

Answer 1

Step-by-step explanation:

AB = 5*Square root of 2 cm

BC = 4*Square root of 2 cm

CD = 5*Square root of 2 cm

DA = 4*Square root of 2 cm

Opposite sides of ABCD are equal

So, ABCD is a parallelogram

Answer 2

Answer:

Given quadrilateral is Rectangle.

Step-by-step explanation:

Given points are A(2,-2),B(7,3),C(11,-1) and D(6,-6)

We know that distance between points (x₁,y₁) and (x₂,y₂) is given by distance

= √(x₂ - x₁)² + (y₂ - y₁)²

Now,

AB = √(7 - 2)² + (3 + 2)²

     = √50

     = 5√2 units

BC = √(11 - 7)² + (-1 - 3)²

     = √32

     = 4√2 units

CD = √(11 - 7)² + (-1 - 3)²

     = √32

     = 4√2 units

DA = √(2 - 6)² + (-2 + 6)²

     = √32

     = 4√2 units

AC = √(11 - 2)² + (-1 + 2)²

     = √82

BD = √(6 - 7)² + (-6 - 3)²

     = √82 units

Here, we see that the sides AB = CD and BC = DA.

Also, diagonals are equal i.e., AC = BD

which shows the quadrilateral is a rectangle.

Therefore,

Given quadrilateral is Rectangle.

Hope it helps!