Question

Graph the points in the figure below, and find the perimeter of each shape. Round to the nearest tenth if necessary. (1,-4), (3,-4), (4, -3), (1, -2)

Answer 1

graphing

to find the perimeter we need the measure of each side

we can use the formula to find the distance

`d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}`

where (x1,y1) and (x2,y2) are the coordinates of each point

Side AB

`\begin{gathered} \sqrt[]{(1-4)^2+((-2)-(-3))^2} \\ \\ \sqrt[]{-3^2+1^2} \\ \\ AB=\sqrt[]{10} \end{gathered}`

Side BC

`\begin{gathered} \sqrt[]{(4-3)^2+((-3)-(-4))^2} \\ \\ \sqrt[]{1^2+1^2} \\ \\ BC=\sqrt[]{2} \end{gathered}`

Side CD

`\begin{gathered} \sqrt[]{(3-1)^2+((-4)-(-4))^2} \\ \\ \sqrt[]{2^2+0^2} \\ \\ CD=2 \end{gathered}`

Side DA

`\begin{gathered} \sqrt[]{(1-1)^2+((-4)-(-2))^2} \\ \\ \sqrt[]{0^2+(-2)^2} \\ \\ DA=2 \end{gathered}`

now, sum the sides

`\begin{gathered} P=AB+BC+CD+DA \\ P=\sqrt[]{10}+\sqrt[]{2}+2+2 \\ P=8.576 \end{gathered}`

rounding the perimeter is 8.6 units