Question

calculator
the coordinates of the vertices of a rectangle are (-4, 3), (-1, 5), (3, -1), and (0, -3).
what is the perimeter of the rectangle? round each step to the nearest tenth.
enter your answer as a decimal in the box.

Explanation:

Step1: Calculate length of first side

Use distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Take $(-4,3)$ and $(-1,5)$:
$d_1=\sqrt{(-1-(-4))^2+(5-3)^2}=\sqrt{3^2+2^2}=\sqrt{13}\approx3.6$

Step2: Calculate length of adjacent side

Take $(-1,5)$ and $(3,-1)$:
$d_2=\sqrt{(3-(-1))^2+(-1-5)^2}=\sqrt{4^2+(-6)^2}=\sqrt{52}\approx7.2$

Step3: Compute perimeter

Perimeter $P=2(d_1+d_2)=2(3.6+7.2)=2×10.8=21.6$

Answer:

21.6