sort the following transformations into two categories: transformations that preserve distance and angle measures and transformations that do not preserve distance, but preserve angle measures.
- a 90° counter - clockwise rotation about the origin
- a translation that moves a figure to the right and up
- a reflection over the line x = 0
- a dilation centered at the origin with a scale factor of $\frac{1}{2}$
- a clockwise rotation about the point (2, - 1).
- a translation that moves a figure to the left and up.
- a translation that moves a figure from quadrant i to quadrant iii
- a dilation centered at (1, 1) with a scale factor of 3.
- a reflection over the x - axis

preserve distance and angle measures | preserve angle measures but not distance

Question

sort the following transformations into two categories: transformations that preserve distance and angle measures and transformations that do not preserve distance, but preserve angle measures.
- a 90° counter - clockwise rotation about the origin
- a translation that moves a figure to the right and up
- a reflection over the line x = 0
- a dilation centered at the origin with a scale factor of $\frac{1}{2}$
- a clockwise rotation about the point (2, - 1).
- a translation that moves a figure to the left and up.
- a translation that moves a figure from quadrant i to quadrant iii
- a dilation centered at (1, 1) with a scale factor of 3.
- a reflection over the x - axis

preserve distance and angle measures | preserve angle measures but not distance

Accepted Answer

# Explanation:
## Step1: Recall properties of transformations
Rigid - motions (isometries) preserve distance and angle measures. These include rotations, translations, and reflections. Dilations change the size (distance between points) but preserve angle measures.
## Step2: Categorize each transformation
- **Rotations**: A 90° counter - clockwise rotation about the origin, a clockwise rotation about the point (2, - 1) are rotations. They preserve distance and angle measures.
- **Translations**: A translation that moves a figure to the right and up, a translation that moves a figure to the left and up, a translation that moves a figure from quadrant I to quadrant III are translations. They preserve distance and angle measures.
- **Reflections**: A reflection over the line x = 0, a reflection over the x - axis are reflections. They preserve distance and angle measures.
- **Dilations**: A dilation centered at the origin with a scale factor of $\frac{1}{2}$, a dilation centered at (1, 1) with a scale factor of 3 are dilations. They preserve angle measures but not distance.

# Answer:
| Preserve distance and angle measures | Preserve angle measures but not distance |
| --- | --- |
| A 90° counter - clockwise rotation about the origin | A dilation centered at the origin with a scale factor of $\frac{1}{2}$ |
| A translation that moves a figure to the right and up | A dilation centered at (1, 1) with a scale factor of 3 |
| A reflection over the line x = 0 |  |
| A clockwise rotation about the point (2, - 1) |  |
| A translation that moves a figure to the left and up |  |
| A translation that moves a figure from quadrant I to quadrant III |  |
| A reflection over the x - axis |  |

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QUESTION IMAGE

Question

Explanation:

Step1: Recall properties of transformations

Step2: Categorize each transformation

Answer:

Preserve distance and angle measures	Preserve angle measures but not distance
A translation that moves a figure to the right and up	A dilation centered at (1, 1) with a scale factor of 3
A reflection over the line x = 0
A clockwise rotation about the point (2, - 1)
A translation that moves a figure to the left and up
A translation that moves a figure from quadrant I to quadrant III
A reflection over the x - axis