Question

Triangle QRS is dilated according to the rule DO,2 (x,y).

On a coordinate plane, (0, 0) is the center of dilation. Triangle Q R S has points (negative 3, 3), (2, 4), and (negative 1, 1).

What is true about the image ΔQ'R'S'? Select three options.

Which statements are true?

DO,2 (x,y) = (2x, 2y)
Side Q'S' lies on a line with a slope of -1.
QR is longer than Q'R'.
The vertices of the image are closer to the origin than those of the pre-image.
The distance from Q' to the origin is twice the distance from Q to the origin.

Answer 1

True statements:
- DO,2 (x,y) = (2x, 2y). (Dilation about the origin with scale factor 2 multiplies coordinates by 2.)
- Side Q'S' lies on a line with a slope of -1. (Q' = (-6,6), S' = (-2,2); slope = (2-6)/(-2+6) = -4/4 = -1.)
- The distance from Q' to the origin is twice the distance from Q to the origin. (Scaling by 2 doubles all distances from the center: |Q'0| = 2|Q0|.)

The other two statements are false. QR is shorter than Q'R' (image lengths are doubled), and the image vertices are farther from the origin, not closer.