A farmer built a new fence around a rectangular field. The corner posts are located at points (2, 3), (2, −5), (−4, −5), and (−4, 3) on a coordinate plane. In the middle of the field at the point where the diagonals intersect, the farmer wants to build a light post. What are the coordinates of the light post?
(1, −1)
(−1, 3)
(−1, −1)
(−4, −1)
The point where the diagonals of a rectangle intersect is the midpoint of the diagonals. Since the diagonals of a rectangle are equal in length and bisect each other, the point where they intersect is the midpoint.
The midpoint formula is:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case, the midpoint is:
((2 - 4) / 2, (3 - 5) / 2)
= ((-2) / 2, (-2) / 2)
= (-1, -1)
Therefore, the coordinates of the light post at the point where the diagonals intersect are (-1, -1). So, the correct answer is (−1, −1).