Carterville was built along a grid using a coordinate plane. City Hall was located at (1, 4) . The Fire Department was located at (-3, 4) and the Police Department was located at (1, -2). Each square on the coordinate plane is equal to 1 square mile. City planning wants to build a park such that the shape created by the Fire Department, City Hall and the Police Department form a rectangle. What should the coordinates of the new park be?

Question

A. (-2,-3)

B. (-3,-2)

C. (0,0)

D. (-1,-4)

Answer 1

To find the coordinates of the new park that, along with the Fire Department (-3, 4) and City Hall (1, 4) and the Police Department (1, -2), form a rectangle, we need to determine the fourth vertex of the rectangle.

Given the points:

• City Hall (1, 4)
• Fire Department (-3, 4)
• Police Department (1, -2)

We can note that the Fire Department and City Hall share the same y-coordinate (4), indicating they are on the same horizontal line. The Police Department has the same x-coordinate (1) as City Hall, if we look for symmetry in the arrangement.

The coordinates of the missing fourth vertex can be deduced by maintaining the rectangular structure:

• The x-coordinate of the fourth point must match that of the Fire Department (-3).
• The y-coordinate must match that of the Police Department (-2).

Thus, the coordinates of the new park should be (-3, -2).

Therefore, the answer is:

B. (-3, -2)