What type of a quadrilateral do the points A(2,-2),B(7,3),C(11,-1)andD(6,-6)
taken in thatborder form?
Answers
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:
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!