https://file.aiquickdraw.com/mathbot/file/1729182974563rvbjc2lo.jpg

Let's work through the questions in the image you've uploaded. Here's a breakdown of the problems:

### Problem 6:
**Reflection of point G(5, 3) over the x-axis:**

When a point is reflected over the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. So the coordinates of the reflected point \( G' \) will be:
\[
G'(5, -3)
\]

### Problem 7:
**Reflection of point T(1, 6) over the line \( y = x \):**

When reflecting a point over the line \( y = x \), the x- and y-coordinates are swapped. So the coordinates of the reflected point \( T' \) will be:
\[
T'(6, 1)
\]

### Problem 8:
This problem asks you to write a reflection rule for mapping each triangle to its image:

#### Part (a):
Points are given as \( J(1, 0), K(-5, 2), L(4, -4) \), and their corresponding reflected points \( J'(-9, 0), K'(-5, -2), L'(4, 4) \).

By examining the changes in the coordinates:
- For \( J \) to \( J' \), the reflection occurs over the line \( x = -4 \).
- For \( K \) to \( K' \), the y-coordinate changes sign, which is a reflection over the x-axis.
- For \( L \) to \( L' \), the y-coordinate also changes sign.

So the reflection seems to be over the x-axis.

#### Part (b):
Points are given as \( P(8, 6), Q(-4, 12), R(7, 7) \), and their corresponding reflected points \( P'(8, -20), Q'(-4, -12), R'(7, -7) \).

Here, it seems that the reflection is happening over the x-axis again, since all the y-coordinates are changing sign.

---

Would you like further details or clarification on any of these steps?

### Relative Questions:
1. How would the reflection of a point over the y-axis change the coordinates?
2. How do you reflect a point over a diagonal line like \( y = -x \)?
3. What are the properties of a rigid transformation, and why is a size change not a rigid motion?
4. Could you reflect a figure over an arbitrary line, like \( y = 2x + 1 \)? How would you do it?
5. How can you determine whether a transformation is a rotation or reflection based only on the coordinates?

### Tip:
For reflections over the x-axis or y-axis, remember to only change the sign of one coordinate: the y-coordinate for reflections over the x-axis and the x-coordinate for reflections over the y-axis.

What are the coordinates of reflected points for different transformations, including reflection over the x-axis and over the line y = x?

Learn how to solve geometry problems involving reflections. This problem includes reflecting points over the x-axis and the line y = x, with detailed solutions and key formulas for understanding transformations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation