Question

a warehouse manager wants to redesign the warehouse shipping area. the manager creates a scale drawing of the warehouse on a coordinate plane. the shipping area is in the shape of a trapezoid with vertices at (j(-6,3)), (k(0, - 4)), (l(4, - 6)), and (m(-8, - 14)). what is the perimeter of the shipping area in the scale drawing? round the answer to the nearest tenth if necessary. enter your answer in the box. units

Explanation:

Step1: Use 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 $JK$

For points $J(-6,3)$ and $K(0, - 4)$, we have $x_1=-6,y_1 = 3,x_2=0,y_2=-4$.
$d_{JK}=\sqrt{(0 + 6)^2+(-4 - 3)^2}=\sqrt{36 + 49}=\sqrt{85}\approx9.2$.

Step3: Calculate length of $KL$

For points $K(0,-4)$ and $L(4,-6)$, we have $x_1 = 0,y_1=-4,x_2=4,y_2=-6$.
$d_{KL}=\sqrt{(4 - 0)^2+(-6 + 4)^2}=\sqrt{16+4}=\sqrt{20}=2\sqrt{5}\approx4.5$.

Step4: Calculate length of $LM$

For points $L(4,-6)$ and $M(-8,-14)$, we have $x_1 = 4,y_1=-6,x_2=-8,y_2=-14$.
$d_{LM}=\sqrt{(-8 - 4)^2+(-14 + 6)^2}=\sqrt{144 + 64}=\sqrt{208}=4\sqrt{13}\approx14.4$.

Step5: Calculate length of $MJ$

For points $M(-8,-14)$ and $J(-6,3)$, we have $x_1=-8,y_1=-14,x_2=-6,y_2 = 3$.
$d_{MJ}=\sqrt{(-6 + 8)^2+(3 + 14)^2}=\sqrt{4+289}=\sqrt{293}\approx17.1$.

Step6: Calculate perimeter

$P=d_{JK}+d_{KL}+d_{LM}+d_{MJ}\approx9.2 + 4.5+14.4+17.1 = 45.2$.

Answer:

$45.2$