Question

Rhombus STAR has vertices S(-1,2), T(2,3), A(3,0), and R(0,-1).What is the perimeter of rhombus STAR?ABCD√344√34√104√10

Answer 1

INFORMATION:

We know that:

- Rhombus STAR has vertices S(-1,2), T(2,3), A(3,0), and R(0,-1)

And we must calculate the perimeter of the rhombus

STEP BY STEP EXPLANATION:

To calculate it, we must find first the measure of one of the sides.

We can find one of the sides calculating the distance between two consecutive vertices.

So, calculating the distance between vertices S and T

$\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt{(2-(-1))^2+(3-2)^2} \\ d=\sqrt{3^2+1^2} \\ d=\sqrt{10} \end{gathered}$

Finally, to find the perimeter, we need to use that the rhombus has 4 equal sides. So, we the perimeter would be

$\begin{gathered} perimeter=4\times\sqrt{10} \\ perimeter=4\sqrt{10} \end{gathered}$

ANSWER:

D. 4√10