Question

Choose the best selection for the

parallelogram with vertices at the
following points.
(-5,5), (4,2), (3,-1), (-6,2)

A. Rectangle
B. Square
C. Rhombus
D. None​

Answer 1

The vertices form s rectangle.

Explanation:

Given,

Let, four vertices are A(-5,5), B(4,2), C(3,1), D(-6,2)

To find out ABCD will be A type of quadrilateral

Formula

The length of two points (
`x_(1)`,
`y_(1)`) and (
`x_(2) ,y_(2)`) is
`\sqrt{(x_(2)-x_(1) )^(2) +(y_(2)-y_(1) )^(2) }`

Here,

AB ⇒
`\sqrt{(4+5)^(2) +(2-5)^(2) }` =
`√(90)` [
`x_(1) =-5,y_(1) =5,x_(2)=4 ,y_(2)=2`]

BC ⇒
`\sqrt{(3-4)^(2) +(-1-2)^(2) }` =
`√(10)` [
`x_(1)=4, y_(1)=2, x_(2)=3, y_(2)=-1`]

CD ⇒
`\sqrt{(-6-3)^(2)+(2+1)^(2) }` =
`√(90)` [
`x_(1)=3, y_(1)=-1, x_(2)=-6, y_(2)=2]`

DA ⇒
`\sqrt{(-5+6)^(2)+(5-2)^(2) }` =
`√(10)` [
`x_(1)=-6, y_(1)=2, x_(2)=-5, y_(2)= 5`

So,

AB= CD and BC = DA

Hence, it is a rectangle.

Answer 2

A. Rectangle

Explanation:

Just Place points (-5,5), (4,2), (3,-1), (-6,2) on the coordinates plane

and you’ll get a rectangle.

check the picture below.