Question

Plot the points A(-11,4), B(3, 7), C(6, -7) on the coordinate axes below. State the coordinates of point DD such that AA, BB, CC, and DD would form a rectangle. (Plotting point DD is optional.)
Click on the graph to plot a point. Click a point to delete it.
x

Answer 1

If A, B, C are consecutive vertices of the rectangle (A → B → C → D), then D = A + C − B.

Compute:
- x: −11 + 6 − 3 = −8
- y: 4 + (−7) − 7 = −10

So D = (−8, −10).

Quick check: AB = (14, 3) and BC = (3, −14); AB · BC = 14·3 + 3·(−14) = 0 so AB ⟂ BC, and CD = −AB, AD = BC, so ABCD is a rectangle.

You can plot D at (−8, −10).