graphing
to find the perimeter we need the measure of each side
we can use the formula to find the distance
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]where (x1,y1) and (x2,y2) are the coordinates of each point
Side AB
[tex]\begin{gathered} \sqrt[]{(1-4)^2+((-2)-(-3))^2} \\ \\ \sqrt[]{-3^2+1^2} \\ \\ AB=\sqrt[]{10} \end{gathered}[/tex]Side BC
[tex]\begin{gathered} \sqrt[]{(4-3)^2+((-3)-(-4))^2} \\ \\ \sqrt[]{1^2+1^2} \\ \\ BC=\sqrt[]{2} \end{gathered}[/tex]Side CD
[tex]\begin{gathered} \sqrt[]{(3-1)^2+((-4)-(-4))^2} \\ \\ \sqrt[]{2^2+0^2} \\ \\ CD=2 \end{gathered}[/tex]Side DA
[tex]\begin{gathered} \sqrt[]{(1-1)^2+((-4)-(-2))^2} \\ \\ \sqrt[]{0^2+(-2)^2} \\ \\ DA=2 \end{gathered}[/tex]now, sum the sides
[tex]\begin{gathered} P=AB+BC+CD+DA \\ P=\sqrt[]{10}+\sqrt[]{2}+2+2 \\ P=8.576 \end{gathered}[/tex]rounding the perimeter is 8.6 units
