Question

Max is drawing plans for a garden, measured in feet, which is shown below on the coordinate plane. Max has two vertices of the garden at points (-1, 2) and (-1, -2). On a coordinate plane, points (-1, 2) and (-1, -2) are plotted. At which points should Max have the other two vertices in order to make the area of his garden 20 square feet?

1) (2, -2) and (2, 2)
2) (4, -2) and (4, 2)
3) (3, -2) and (3, 2)
4) (5, -2) and (5, 2)

Answer 1

To make the area of the garden 20 square feet, Max should have the other two vertices of the garden at points (4, -2) and (4, 2). Hence the correct answer is option 2

Step-by-step explanation:

To find the other two vertices of Max's garden, we need to determine the dimensions of the garden. Since the two given vertices are (-1, 2) and (-1, -2), we can calculate the length of the rectangle by finding the vertical distance between the two points, which is 2 - (-2) = 4 feet. To make the area of the garden 20 square feet, we need to find the width of the rectangle.

Since the area of a rectangle is given by the formula length x width, we can rearrange the formula to solve for the width. In this case, the length is 4 feet and the area is 20 square feet. So, width = area / length = 20 / 4 = 5 feet.

Therefore, the other two vertices of Max's garden should be located 5 feet away horizontally from the given vertices. The options provided are (2, -2) and (2, 2), (4, -2) and (4, 2), (3, -2) and (3, 2), and (5, -2) and (5, 2). Among these options, the correct ones are (4, -2) and (4, 2) because they are 5 feet away from the given vertices horizontally.

Hence the correct answer is option 2