We are given a quadrilateral, and we are asked to find the length of one of its sides. To do that, let's remember the formula for the length of a line segment in a coordinated plane:
[tex]L=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Where:
[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]
Are the extreme points of the line segment. Therefore, we need to find the coordinates of points A and B. These are:
[tex]\begin{gathered} A=(-2,6) \\ B=(4,3) \end{gathered}[/tex]
Now we replace these values in the formula:
[tex]L=\sqrt[]{(3-6)^2+(4-(-2))^2}[/tex]
Solving the operations:
[tex]L=\sqrt[]{(-3)^2+(6)^2}[/tex][tex]L=\sqrt[]{9+36}=\sqrt[]{45}=6.7[/tex]
Therefore, the length is 6.7
