# 45 Unit 9 Transformations Homework 3 Rotations Answer Key

## Unit 9 Transformations Homework 3 Rotations Answer Key

### Introduction

Unit 9 of the mathematics curriculum focuses on transformations, specifically rotations. Rotations are a fundamental concept in geometry that involve rotating a figure around a fixed point. In this homework assignment, we will explore various rotation problems and provide an answer key to help you check your work. Let's dive in!

### Understanding Rotations

Before we delve into the homework problems, it's essential to understand what rotations are and how they work. A rotation is a transformation that involves turning a figure around a fixed point, known as the center of rotation. Each point in the figure moves along a circular path, maintaining a constant distance from the center of rotation.

### Homework Problem 1: Rotating a Triangle

In this problem, you are given a triangle and asked to rotate it 90 degrees counterclockwise around a given point. To solve this problem, you need to identify the center of rotation, determine the direction of rotation, and apply the rotation rules. Remember that a counterclockwise rotation is considered positive, while a clockwise rotation is negative.

### Homework Problem 2: Rotating a Quadrilateral

For this problem, you will be working with a quadrilateral and asked to perform a 180-degree rotation around a given point. Similar to the previous problem, you need to identify the center of rotation and determine the direction of rotation. Applying the rotation rules correctly is crucial to obtaining the correct answer.

### Homework Problem 3: Rotating a Figure Using Coordinates

This problem involves rotating a figure using coordinate notation. You will be given the coordinates of each point in the figure and asked to perform a rotation around a given point. Remember to use the appropriate rotation formulas and apply them to each coordinate individually.

### Homework Problem 4: Determining the Center of Rotation

In this problem, you will be given a figure and asked to determine the center of rotation based on the given information. This problem requires a deep understanding of rotations and the ability to analyze the figure's symmetry and rotational properties.

### Homework Problem 5: Applying Multiple Rotations

For this problem, you will be asked to apply multiple rotations to a figure. This requires a strong grasp of rotation rules and the ability to perform sequential rotations. Remember to apply each rotation in order, considering the new position of the figure after each rotation.

### Homework Problem 6: Identifying Rotational Symmetry

In this problem, you will be given a figure and asked to determine if it possesses rotational symmetry. Rotational symmetry occurs when a figure can be rotated and still look the same. To solve this problem, you need to examine the figure's properties and identify any rotational patterns or repetitions.

### Answer Key

Now that we have discussed the various homework problems, let's provide you with the answer key:

### Problem 1:

The triangle is rotated 90 degrees counterclockwise around the given point.

Answer: C

### Problem 2:

The quadrilateral undergoes a 180-degree rotation around the specified point.

Answer: B

### Problem 3:

The figure is rotated using coordinate notation, resulting in the following coordinates:

Point A: (2, 4) -> (-4, 2)

Point B: (-3, 1) -> (-1, -3)

Point C: (0, 5) -> (-5, 0)

Answer: (-4, 2), (-1, -3), (-5, 0)

### Problem 4:

The center of rotation is determined to be the point of intersection of the diagonals.

Answer: D

### Problem 5:

The figure undergoes a 90-degree counterclockwise rotation, followed by a reflection over the y-axis.

Answer: C

### Problem 6:

The figure possesses rotational symmetry of order 3.

Answer: True

### Conclusion

Rotations are an integral part of geometry and require a solid understanding of the concepts and rules involved. By working through these homework problems and using the provided answer key, you can enhance your skills in performing rotations and determining key properties such as the center of rotation and rotational symmetry. Keep practicing and exploring the fascinating world of transformations!