Question

You are graphing Rectangle ABCD in the coordinate plane. The following are three of the vertices of the

rectangle A(-7.-2), B(3.–2), and C(3,-5).
What are the coordinates of point D?

Answer 1

D(-7, -5)

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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Comment on the solution

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.