Question

On a coordinate plane, the center of dilation is at (0, 0). Triangle A B C has points (negative 4, 3), (4, 4), and (1, 1).
A has the coordinates (–4, 3) and B has the coordinates (4, 4). If DO,1/2(x, y) is a dilation of △ABC, what is true about the image △A'B'C'? Check all that apply.

AB is parallel to A'B'.
DO,1/2(x, y) = (one-half x, one-half y)
The distance from A' to the origin is half the distance from A to the origin.
The vertices of the image are farther from the origin than those of the pre-image.
A'B' is greater than AB.

Answer 1

True:
- AB is parallel to A'B'. (A dilation about the origin preserves direction/parallelism.)
- DO,1/2(x,y) = (1/2 x, 1/2 y).
- The distance from A' to the origin is half the distance from A to the origin. (Lengths from the center scale by 1/2.)

False:
- The vertices of the image are farther from the origin than those of the pre-image. (They are closer.)
- A'B' is greater than AB. (A'B' = 1/2·AB, so it is smaller.)

(For reference A' = (−2, 1.5), B' = (2, 2), C' = (0.5, 0.5).)