Question

complete the sentence so that the sequence of transformations will not preserve distance. a horizontal translation that moves a figure from quadrant ii to quadrant i, then a clockwise rotation. vertical translation. reflection over the x - axis. dilation with a scale factor of two. a b c d select the transformation function(s) that represent a rigid motion. (x,y)→(1/2 x,y) (x,y)→(−y,−x) (x,y)→(1.5x,1.5y) (x,y)→(x - 6,y + 1/2) (x,y)→(7 + x,3 + y) a b c d e

Explanation:

Step1: Recall properties of transformations

Rigid - motions preserve distance and shape. Translations and rotations are rigid - motions. Dilations change the size of a figure and do not preserve distance.

Step2: Analyze the first question

A dilation with a scale factor of two changes the size of the figure, so it does not preserve distance. Translations (horizontal and vertical) and rotations preserve distance. Reflection over the x - axis is also a rigid - motion. So for the first question, the answer is dilation with a scale factor of two.

Step3: Analyze the second question

For the transformation functions:

• $(x,y)\to(\frac{1}{2}x,y)$ and $(x,y)\to(1.5x,1.5y)$ are dilations and not rigid - motions.
• $(x,y)\to(-y, - x)$ is a rotation (90 - degree counter - clockwise rotation about the origin), which is a rigid - motion.
• $(x,y)\to(x - 6,y+\frac{1}{2})$ and $(x,y)\to(7 + x,3 + y)$ are translations, which are rigid - motions.

Answer:

1. D. dilation with a scale factor of two
2. B. $(x,y)\to(-y, - x)$

D. $(x,y)\to(x - 6,y+\frac{1}{2})$
E. $(x,y)\to(7 + x,3 + y)$