https://file.aiquickdraw.com/mathbot/file/1727198449635ay4jnbw1.jpg

To solve this problem, we will break it into two transformations as specified: 

1. **Reflection across the line \( y = 1 \)**.
2. **Rotation 180° counterclockwise around the origin**.

### Step 1: Reflection across the line \( y = 1 \)
We need to reflect the coordinates of points \( G \), \( H \), and \( I \) across the horizontal line \( y = 1 \). 

- The formula for reflecting a point \( (x, y) \) across a horizontal line \( y = k \) is:
  \[
  (x', y') = (x, 2k - y)
  \]
  In this case, \( k = 1 \).

### Step 2: 180° Rotation Counterclockwise Around the Origin
After reflection, we will rotate the new points 180° counterclockwise around the origin. The formula for rotating a point \( (x, y) \) by 180° counterclockwise is:
  \[
  (x', y') = (-x, -y)
  \]

Let me now apply these transformations to the triangle's points and plot the resulting image.

Graph the image of ΔGHI after the following sequence of transformations: Reflection across the line y = 1, Rotation 180° counterclockwise around the origin.

Explore how to graph the image of ΔGHI after reflecting it across the line y = 1 and rotating it 180° counterclockwise around the origin. This problem involves key geometric transformation concepts and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation