Question

find the perimeter of quadrilateral rstu in the coordinate plane. round your answer to the nearest tenth place if necessary. s(-4,4) t(3,3) r(-4,-1) u(2,-1)

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 $RS$

For points $R(-4,-1)$ and $S(-4,4)$, $x_1=-4,y_1 = - 1,x_2=-4,y_2 = 4$.
$RS=\sqrt{(-4+4)^2+(4 + 1)^2}=\sqrt{0 + 25}=5$.

Step3: Calculate $ST$

For points $S(-4,4)$ and $T(3,3)$, $x_1=-4,y_1 = 4,x_2=3,y_2 = 3$.
$ST=\sqrt{(3 + 4)^2+(3 - 4)^2}=\sqrt{49+1}=\sqrt{50}\approx7.1$.

Step4: Calculate $TU$

For points $T(3,3)$ and $U(2,-1)$, $x_1=3,y_1 = 3,x_2=2,y_2 = - 1$.
$TU=\sqrt{(2 - 3)^2+(-1 - 3)^2}=\sqrt{1 + 16}=\sqrt{17}\approx4.1$.

Step5: Calculate $UR$

For points $U(2,-1)$ and $R(-4,-1)$, $x_1=2,y_1 = - 1,x_2=-4,y_2 = - 1$.
$UR=\sqrt{(-4 - 2)^2+(-1+1)^2}=\sqrt{36+0}=6$.

Step6: Calculate perimeter

Perimeter $P=RS + ST+TU+UR$.
$P=5 + 7.1+4.1+6=22.2$.

Answer:

$22.2$