Question

Plot the points A(-4,-5), B(6, 1), C(-1, 4) on the coordinate axes below. State the coordinates of point DD such that AA, BB, CC, and DD would form a parallelogram.

Answer 1

Answer:

  D(-11, -2)

Step-by-step explanation:

You want the coordinates of point D so that ABCD is a parallelogram, given A(-4, -5), B(6, 1), C(-1, 4).

Midpoint

The midpoints of the diagonals are the same point:

  (A +C)/2 = (B +D)/2

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

  D = A +C -B . . . . . . solve for D

  D = (-4, -5) +(-1, 4) -(6, 1) = (-4 -1 -6, -5 +4 -1) = (-11, -2)

The coordinates of point D are (-11, -2).