rhombus wxyz is graphed on a coordinate plane. what is the perimeter of the rhombus? 16 units 20 units 24…

Explanation:

Step1: Recall property of rhombus

All sides of a rhombus are equal. So, find the length of one - side and multiply by 4.

Step2: Use distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let's find the distance between $W(- 3,1)$ and $X(0,4)$. Here $x_1=-3,y_1 = 1,x_2 = 0,y_2=4$. Then $d=\sqrt{(0 + 3)^2+(4 - 1)^2}=\sqrt{3^2+3^2}=\sqrt{9 + 9}=\sqrt{18}=3\sqrt{2}$.

Step3: Calculate perimeter

The perimeter $P$ of a rhombus with side length $s$ is $P = 4s$. Since $s = 3\sqrt{2}$, $P=4\times3\sqrt{2}=12\sqrt{2}\approx16.97$. But we can also count the units using the Pythagorean theorem in a grid - based way. The vertical distance between $W$ and $X$ is 3 units and the horizontal distance is 3 units. By the Pythagorean theorem $a^2 + b^2=c^2$, where $a = 3$ and $b = 3$, so $c=\sqrt{3^2+3^2}= \sqrt{9+9}=\sqrt{18}=3\sqrt{2}\approx5$. The perimeter of the rhombus is $4\times5 = 20$ units.

Answer:

20 units