Answer:
D(-7, -5)
Step-by-step explanation:
There are a couple of ways to figure this.
1) When the rectangle is aligned with the axes, as this one is, each coordinate value shows up twice. In the given list, x-values of 3 are repeated, but -7 is not, so the x-coordinate is -7.
The y-values of -2 are repeated, but -5 is not, so the y-coordinate is -5.
The coordinates of point D are (-7, -5).
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2) The midpoint of diagonal AC is the same as the midpoint of diagonal BD, so the sum of coordinates at the ends of the diagonals will be the same:
A+C = B+D
Subtracting the coordinates of B from the sum of A and C will give you the coordinates of D:
D = A +C -B = (-7, -2) +(3, -5) -(3, -2) = (-7+3-3, -2-5+2)
D = (-7, -5)
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<em>Comment on the solution</em>
The second approach works with any parallelogram, rhombus, rectangle, or square--any figure in which the diagonals bisect each other. The figure does not have to be aligned with the axes, as it does in the first approach.
