Question

name the type of quadrilateral formed by the vertices (-2,0)(3,2)(2,-1) and(-3,-3) give reasons​

Answer 1

Answer: Parallelogram

The Figure when formed by joining the vertices is a Parallelogram.

Reasons:

1) Both pairs of opposite sides are equal in length

2) Slope of opposite sides:

i) Points: (-2,0), (3,2) & (-3,-3), (2,-1)

Slope: 2/5 and 2/5

They are Parallel

ii) Points: (-2,0), (-3,-3) & (3,2), (2,-1)

Slope: 3/-1 and -3/1

They are Parallel as well

Answer 2

Therefore it is a parallelogram.

Step-by-step explanation:

Given vertices of the quadrilateral are A(-2,0),B (3,2), C(2,-1) and D(-3,-3)

The length of AB is =$\sqrt{(-2-3)^2+(0-2)^2}$ =$\sqrt{29}$ units

The length of BC is =$\sqrt{(3-2)^2+(2+1)^2}$ =$\sqrt{10}$units

The length of CD is $\sqrt{(2+3)^2+(-1+3)^2}$=$\sqrt{29}$units

The length of AD is =$\sqrt{(-3+2)^2+(-3-0)^2}$=$\sqrt{10}$units

The length of diagonal AC is=$\sqrt{(-2-2)^2+(0+1)^2}$=$\sqrt{17}$units

The length of diagonal BD is $\sqrt{(3+3)^2+(2+3)^2}$ =$\sqrt{34}$units

Since the parallel sides of the quadrilateral are congruent but the diagonals are not equal.

Therefore it is a parallelogram.