Question

in the diagram, △abc ≅ △wrs. what is the perimeter of △wrs? 13 units 11 units 10 units 12 units

Explanation:

Step1: Find side - lengths of △WRS using distance formula or counting grid units.

$WR=\sqrt{(2 - 0)^2+(1+1)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\approx 2.83$ (using distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$), or by counting grid units (right - triangle with legs 2 and 2). $RS=\sqrt{(4 - 2)^2+( - 1-1)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\approx 2.83$. $WS = 5$ (counting grid units as it is a horizontal line segment from $x = 0$ to $x = 5$).

Step2: Calculate the perimeter of △WRS.

$P=WR + RS+WS=2\sqrt{2}+2\sqrt{2}+5 = 4\sqrt{2}+5\approx4\times1.414 + 5=5.656+5 = 10.656\approx11$.

Answer:

11 units