The length of the side WX is [tex]\sqrt{5}[/tex] units.
The length of the side YZ is [tex]\sqrt{5}[/tex] units.
The length of the side XY is [tex]\sqrt{20}[/tex] units.
The length of the side WZ is [tex]\sqrt{20}[/tex] units.
Quadrilateral;
A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices, and four angles.
It is formed by joining four non-collinear points.
Given
Quadrilateral WXYZ has vertices W(-2,1), X(-1,3), Y(3,1), and Z(2,-1).
Distance formula;
The distance formula is used to find the distance between two points.
[tex]\rm Distance \ formula=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
1. The length of the side WX is;
[tex]\rm Distance \ WX=\sqrt{((-1)-(-2))^2+(3-1)^2}\\\\ Distance \ WX=\sqrt{(-1+2)^2+(2)^2}\\\\ Distance \ WX=\sqrt{(1)^2+(2)^2}\\\\ Distance \ WX=\sqrt{1+4}\\\\ Distance \ WX=\sqrt{5}[/tex]
The length of the side WX is [tex]\sqrt{5}[/tex] units.
2. The length of the side YZ is;
[tex]\rm Distance \ YZ=\sqrt{(2-3)^2+(-1-1)^2}\\\\Distance \ YZ=\sqrt{(-1)^2+(-2)^2}\\\\ Distance \ YZ=\sqrt{1+4}\\\\ Distance \ YZ=\sqrt{5}[/tex]
The length of the side YZ is [tex]\sqrt{5}[/tex] units.
3. The length of the side XY is;
[tex]\rm Distance \ XY=\sqrt{(3-(-1))^2+(1-3)^2}\\\\Distance \ XY=\sqrt{(4)^2+(-2)^2}\\\\ Distance \ XY=\sqrt{16+4}\\\\ Distance \ XY=\sqrt{20}[/tex]
The length of the side XY is [tex]\sqrt{20}[/tex] units.
4. The length of the side WZ is;
[tex]\rm Distance \ WZ =\sqrt{(2-(-2))^2+(-1-1)^2}\\\\Distance \ WZ =\sqrt{(4)^2+(-2)^2}\\\\ Distance \ WZ =\sqrt{16+4}\\\\ Distance \ WZ =\sqrt{20}[/tex]
The length of the side WZ is [tex]\sqrt{20}[/tex] units.
To know more about the Distance formula click the link given below.
https://brainly.com/question/71956
