Unit 9 Transformations Homework 1 Answer Key
Introduction
Unit 9 of your math curriculum focuses on transformations, which are fundamental concepts in geometry. In this article, we will provide you with the answer key for Homework 1 in Unit 9, helping you to check your answers and reinforce your understanding of transformations.
Understanding Transformations
Before we dive into the answer key, let's quickly review the basic concepts of transformations. In geometry, a transformation is a process of changing the position, size, or orientation of a figure. There are four main types of transformations:
- Translation: sliding a figure without changing its size or shape
- Reflection: flipping a figure over a line, creating a mirror image
- Rotation: turning a figure around a fixed point, called the center of rotation
- Dilation: resizing a figure by multiplying its dimensions by a scale factor
Homework 1 Questions
Now, let's move on to the answer key for Homework 1 in Unit 9. This homework consists of various questions related to transformations, and we will provide detailed explanations for each question.
Question 1
The first question asks you to perform a translation on a given figure. You are given the original figure and the translation vector. To find the new coordinates of each vertex, you simply add the corresponding coordinates of the translation vector to the original coordinates.
For example, if the translation vector is (3, -2) and the original figure has vertices (1, 4), (3, 6), and (5, 2), the new coordinates after translation would be (4, 2), (6, 4), and (8, 0), respectively.
Question 2
In question 2, you are asked to reflect a figure over a given line. To do this, you need to find the mirror image of each vertex by reflecting it across the line of reflection.
For instance, if the line of reflection is the x-axis and the original figure has vertices (2, 3), (4, 5), and (6, 1), the reflected coordinates would be (2, -3), (4, -5), and (6, -1) respectively.
Question 3
Question 3 focuses on rotations. You are given a figure and the angle of rotation. To rotate a figure around a fixed point, you need to find the new coordinates of each vertex by using the rotation formula.
For example, if the angle of rotation is 90 degrees counterclockwise and the original figure has vertices (1, 1), (2, 3), and (4, 2), the rotated coordinates would be (-1, 1), (-3, 2), and (-2, 4) respectively.
Question 4
The fourth question deals with dilations. You are given a figure and the scale factor. To dilate a figure, you need to multiply the coordinates of each vertex by the scale factor.
For instance, if the scale factor is 2 and the original figure has vertices (1, 2), (3, 4), and (5, 6), the dilated coordinates would be (2, 4), (6, 8), and (10, 12) respectively.
Question 5
The final question in Homework 1 combines multiple transformations. You are asked to perform a sequence of transformations on a figure, such as a translation followed by a rotation or a reflection followed by a dilation.
To solve this type of question, apply each transformation step by step, updating the coordinates of the figure after each transformation.
Conclusion
Transformations are important concepts in geometry, and mastering them is crucial for understanding more complex topics in mathematics. By completing Homework 1 in Unit 9, you have practiced performing different types of transformations and solidified your understanding of the key concepts. We hope this answer key has helped you check your work and further enhance your knowledge of transformations.