https://file.aiquickdraw.com/mathbot/file/1726784114553x2pa5u77.jpg

This image contains six transformation problems involving translations, rotations, and reflections on a coordinate plane. I'll guide you through the transformations based on the grid and shapes shown in the image.

1. **Translation: 5 right and 3 up**
   - The triangle is shifted 5 units to the right and 3 units up from its original position.

2. **Rotation: 180° about the origin**
   - The triangle is rotated 180° around the origin. This means that each point of the triangle will be mapped to its opposite position across the origin.

3. **Rotation: 180° about the origin**
   - Similar to problem 2, this is another rotation by 180° around the origin, resulting in the shape being flipped across both the x- and y-axes.

4. **Translation: 3 left and 5 up**
   - The triangle is shifted 3 units to the left and 5 units up on the coordinate plane.

5. **Reflection: Across the line \( y = 2 \)**
   - The triangle is reflected across the horizontal line \( y = 2 \). Each point will be mirrored with respect to this line.

6. **Reflection: Across the y-axis**
   - The triangle is reflected across the y-axis. This reflection inverts the x-coordinates of the points while keeping the y-coordinates unchanged.

Would you like a more detailed explanation for any specific transformation, or have any questions? Here are some related questions for further practice:

1. How do you find the image of a point after a 90° rotation?
2. What happens to the coordinates of a point after a reflection across the x-axis?
3. How do you determine the new coordinates of a point after a translation of 2 units left and 4 units down?
4. Can you describe how a reflection across the line \( y = -1 \) works?
5. What is the effect of rotating a shape 270° about the origin?

**Tip:** When performing a translation, always add or subtract the translation vector from the original coordinates to find the new position.

The image contains six transformation problems involving translations, rotations, and reflections on a coordinate plane. The goal is to apply each transformation to a triangle shape on a grid.

Learn how to perform transformations on a coordinate plane with translations, rotations, and reflections. This problem set includes translating figures by given vectors, rotating shapes 180° about the origin, and reflecting shapes across lines. Ideal for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation