Rhombus WXYZ is graphed on a coordinate plane with vertices at $(0,0)$, $(4,0)$, $(2,3)$, and $(-2,3)$. What is the perimeter of the rhombus?

• A. $10$
• B. $16$
• C. $14$
• D. $12$

Answer: (B)

Verified step by step guidance

1. Identify the vertices of the rhombus WXYZ as given: W(0,0), X(4,0), Y(2,3), and Z(-2,3).
2. Recall that a rhombus has all sides of equal length, so to find the perimeter, we need to find the length of one side and then multiply by 4.
3. Use the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\): \[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\] to calculate the length of one side, for example, between points W(0,0) and X(4,0).
4. Calculate the distance between W and X by substituting the coordinates into the distance formula: \[d = \sqrt{(4 - 0)^2 + (0 - 0)^2}\].
5. Multiply the length of one side by 4 to find the perimeter of the rhombus: \[\text{Perimeter} = 4 \times d\].