Question

PLEASE HELP SUPER EASY IM JUST STUPID

Which is the most accurate description of the polygon below?

Answer 1

It is a rhombus.

Explanation:

To identify the type of polygon, we will first determine if the opposite sides are parallel. To do this, we find the slope of each line segment. (Parallel lines have the same slope.)

For WX, m = (5-2)/(1-5) = 3/-4 = -3/4

For XY, m = (2--1)/(5-1) = 3/4

For ZY, m = (2--1)/(-3-1) = 3/-4 = -3/4

For ZW, m = (2-5)/(-3-1) = -3/-4 = 3/4

Since the slopes of WX and ZY are the same, these two sides are parallel. Since the slopes of XY and ZW are the same, these two sides are parallel. Since opposite sides are parallel, the figure is a parallelogram.

In order to be a rectangle, the angles would have to be right angles. Since perpendicular lines have slopes that are negative reciprocals of each other, the slopes of adjoining sides would have to be opposite signs and flipped. This is not the case, so the angles are not right; this means it is not a rectangle.

The only other option for a parallelogram without right angles would be a rhombus. This is the case if the length of each side is the same. We will use the distance formula for this:

`WX=√((5-2)^2+(1-5)^2)=√(3^2+(-4)^2)=√(9+16)=√(25)=5\\\\XY=√((2--1)^2+(5-1)^2)=√(3^2+4^2)=√(9+16)=√(25)=5\\\\YZ=√((2--1)^2+(-3-1)^2)=√(3^2+(-4)^2)=√(9+16)=√(25)=5\\\\ZW=√((2-5)^2+(-3-1)^2)=√((-3)^2+(-4)^2)=√(9+16)=√(25)=5`

Since the length of each side is the same, this figure is a rhombus.

Answer 2

It's a rhombus.
1. D
2. A
3. D
4. B
5. C