Question

Plot the points A(10,-3), B(3, -5), C(1, 3) on the

coordinate axes below. State the coordinates of
point D such that A, B, C, and D would form a
parallelogram. (Plotting point D is optional.)
Click on the graph to plot a point. Click a point to delete it.
12
11
y

Answer 1

D(8, 5)

Explanation:

You want the coordinates of point D that completes parallelogram ABCD, where the given points are A(10,-3), B(3, -5), C(1, 3).

Parallelogram

The diagonals of a parallelogram bisect each other, so the midpoint of BD will be the same as the midpoint of AC:

(B+D)/2 = (A+C)/2

B +D = A +C . . . . . . multiply by 2

D = A +C -B . . . . . . subtract B to find D

Using the given coordinates, we have ...

D = (10, -3) +(1, 3) -(3, -5) = (10+1-3, -3+3+5)

D = (8, 5)

The coordinates of point D are (8, 5).

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Additional comment

If we aren't constrained to have parallelogram ABCD, then we can use any pair of given points for the existing diagonal. This gives two other options:

parallelogram ACBD: D(12, -11)

parallelogram ABDC: D(-6, 1)