Question

An engineer is tasked with doubling the length and width of a city park. The engineer draws the park on a coordinate plane and labels it ABCD. Find the area of the park before and after the expansion. A coordinate plane with Square A B C D plotted. Point A is at zero comma three. Point B is at thee comma three. Point C is at three comma zero, Point D is at zero comma zero. What is the area of the park after the length and width are doubled?

Answer 1

First, we need to find the area of the park before the expansion. We can do this by finding the length of one side of the square and then squaring it:

Length of AB = 3 - 0 = 3

Area of ABCD = (Length of AB)^2 = 3^2 = 9

Now, we need to double the length and width of the park. This means that the new coordinates of the vertices will be:

A: (0, 6)

B: (6, 6)

C: (6, 0)

D: (0, 0)

To find the area of the new park, we again need to find the length of one side of the square and then square it:

Length of AB = 6 - 0 = 6

Area of new park = (Length of AB)^2 = 6^2 = 36

Therefore, the area of the park after the length and width are doubled is 36 square units.