Question

The vertices of a rectangle are Q(-1,1), R (5,1), S (5, – 3), and T(-1, -3). What is the point where the diagonals intersect?

A. (2,1)
B. (-1, -1)
C. (2, - 1)
D. (2,0)

Answer 1

The diagonals of a rectangle intersect at the midpoint of either diagonal. The correct midpoint, and thus the intersection point for the rectangle with vertices Q(-1,1), R(5,1), S(5,-3), and T(-1,-3), is (2, -1). the correct answer is (2, -1), which corresponds to option C in the multiple-choice options provided.

Step-by-step explanation:

The question is about finding the point where the diagonals of a rectangle intersect. Since a rectangle is a parallelogram, the diagonals bisect each other. This means that the midpoint of one diagonal is the midpoint of the other diagonal, and this common midpoint is where the diagonals intersect.

To find the midpoint (intersection point) of the diagonals QRS and TR, we need to average the x-coordinates and the y-coordinates of the opposite vertices. Let's calculate:

• Midpoint of QR: ((-1 + 5)/2, (1 + 1)/2) = (2, 1)
• Midpoint of ST: ((5 + -1)/2, (-3 + -3)/2) = (2, -3)

However, since opposite sides of a rectangle are equal, the midpoints calculated should be the same. There's a mistake in the calculation because the y-coordinate should also be the same. Let's correct it: