https://file.aiquickdraw.com/mathbot/file/17266793277396tzbxtnk.jpg

The problem in this image asks for determining the coordinates of points after reflecting two figures over specific axes.

### Part 1: Reflection of ABCDE across the y-axis
When reflecting a point across the **y-axis**, the x-coordinate changes sign while the y-coordinate remains the same.

The original coordinates of figure ABCDE are:
- \( A(6, 6) \)
- \( B(4, 5) \)
- \( C(4, 2) \)
- \( D(2, 2) \)
- \( E(2, 4) \)

The reflected points will be:
- \( A'( -6, 6) \)
- \( B'( -4, 5) \)
- \( C'( -4, 2) \)
- \( D'( -2, 2) \)
- \( E'( -2, 4) \)

### Part 2: Reflection of FGHIJ across the x-axis
When reflecting a point across the **x-axis**, the y-coordinate changes sign while the x-coordinate remains the same.

The original coordinates of figure FGHIJ are:
- \( F(-2, 2) \)
- \( G(-4, 2) \)
- \( H(-4, -1) \)
- \( I(-3, -3) \)
- \( J(-1, -2) \)

The reflected points will be:
- \( F'( -2, -2) \)
- \( G'( -4, -2) \)
- \( H'( -4, 1) \)
- \( I'( -3, 3) \)
- \( J'( -1, 2) \)

Let me know if you'd like further explanation or have questions!

### Five Related Questions:
1. What is the general rule for reflecting a point across the x-axis?
2. How does the reflection change if a figure is reflected across the origin?
3. What is the process for finding the distance between a point and its reflection?
4. Can a reflection across the y-axis and x-axis be combined into one transformation?
5. How do the coordinates change when reflecting across a line other than the x- or y-axis, like \(y = x\)?

**Tip:** Always pay attention to which axis you are reflecting across, as it determines whether the x- or y-coordinate changes.

Find the unknown coordinate for each reflection. Figure ABCDE is reflected across the y-axis to form figure A'B'C'D'E'. Figure FGHIJ is reflected across the x-axis to form figure F'G'H'I'J'.

Learn how to reflect shapes across the x-axis and y-axis in the coordinate plane with a detailed solution. This problem covers key geometry concepts like reflection transformations and is suitable for middle school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation