Given: Quad ABCD with vertices A(­2,2), B(8,­4), C(6,­10) and D(­4,­4). State the coordinates of A'B'C'D', the image of quadrilateral ABCD under D½ . Prove that A'B'C'D' is a parallelogram.

Question

Given: Quad ABCD with vertices A(­2,2), B(8,­4), C(6,­10) and D(­4,­4).

State the coordinates of A'B'C'D', the image of quadrilateral ABCD under D

½ .

Prove that A'B'C'D' is a parallelogram.

Answer 1

Since it's D(1/2), just find the midpoints of each given side..

x y slope distance

A 2 2 1 2.828427125

B 8 4 0.333333333 6.32455532

C 6 -10 7 14.14213562

D 4 4 -7 14.14213562

A' 5 3 0 2

B' 7 -3 -3 6.32455532

C' 5 -3 0 2

D' 3 3 -3 6.32455532

opposite sides are parallel because the slopes are the same,

AND they're equal