Question

a grid map marks the plot of harolds garden in meters. the coordinates of the quadrilateral - shaped property are g(-8, 3), a(4, 8), r(10, 0), and d(-2, -5). he wants to build a short fence around the garden. the perimeter of his garden is meters. 23 36 46 65

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate length of GA

For $G(-8,3)$ and $A(4,8)$, $d_{GA}=\sqrt{(4 + 8)^2+(8 - 3)^2}=\sqrt{144 + 25}=\sqrt{169}=13$.

Step3: Calculate length of AR

For $A(4,8)$ and $R(10,0)$, $d_{AR}=\sqrt{(10 - 4)^2+(0 - 8)^2}=\sqrt{36+64}=\sqrt{100}=10$.

Step4: Calculate length of RD

For $R(10,0)$ and $D(-2,-5)$, $d_{RD}=\sqrt{(-2 - 10)^2+(-5 - 0)^2}=\sqrt{144 + 25}=\sqrt{169}=13$.

Step5: Calculate length of DG

For $D(-2,-5)$ and $G(-8,3)$, $d_{DG}=\sqrt{(-8 + 2)^2+(3 + 5)^2}=\sqrt{36 + 64}=\sqrt{100}=10$.

Step6: Calculate perimeter

Perimeter $P=d_{GA}+d_{AR}+d_{RD}+d_{DG}=13 + 10+13+10 = 46$.

Answer:

46