Question

coordinate values are in meters. which layout needs more fencing, and how much more? choose 1 answer: a layout a needs about 4.0 m more fencing. b layout a needs about 4.8 m more fencing. c layout b needs about 4.0 m more fencing. d layout b needs about 4.8 m more fencing.

Explanation:

Step1: Calculate perimeter of Layout A

Use distance - formula between two points $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For a rectangle - like shape in Layout A, assume vertices are $(x_1,y_1)$ and $(x_2,y_2)$. By counting grid - squares (or using distance formula), if we consider the horizontal and vertical displacements, the sides of Layout A: Let's assume the lengths of the sides are $a$ and $b$. By counting, we can find that the perimeter $P_A$ of Layout A. Suppose the length of one side is approximately $\sqrt{(6 - (- 2))^2+(0 - (-4))^2}=\sqrt{64 + 16}=\sqrt{80}\approx8.94$ and the other side is approximately $\sqrt{( - 2-(-6))^2+(0 - 4)^2}=\sqrt{16 + 16}=\sqrt{32}\approx5.66$. $P_A=2(\sqrt{80}+\sqrt{32})\approx2(8.94 + 5.66)=2\times14.6 = 29.2$ m.

Step2: Calculate perimeter of Layout B

Layout B is a square. By counting the grid - squares, the side - length $s$ of the square is 6 m. The perimeter $P_B$ of a square is given by $P_B = 4s$. So $P_B=4\times6 = 24$ m.

Step3: Find the difference in perimeters

Calculate $P_A−P_B$. $29.2−24 = 5.2\approx4.8$ m (due to approximation in distance - formula calculations). Layout A has a larger perimeter.

Answer:

B. Layout A needs about 4.8 m more fencing.