https://file.aiquickdraw.com/mathbot/file/1726595263085u044b6i3.jpg

The image provided shows two polygons, labeled A and B, on a coordinate plane. The problem asks to complete the transformation rule that maps the pre-image (polygon A) to the image (polygon B). 

To identify the transformation between A and B, we will need to examine:

1. **Reflection**: Check if A and B are mirror images.
2. **Rotation**: Determine if A can be rotated to match B.
3. **Translation**: Look for any shifts in position between the two polygons.
4. **Dilation**: Check if there's any scaling difference between the sizes of A and B.

From a quick observation, it seems the polygons have the same size and shape, which indicates no dilation occurred. They appear to have been rotated. By examining the orientation, it seems like polygon A was rotated **90 degrees counterclockwise** around the origin (0,0) to match polygon B.

The transformation that maps A to B can be described as a **90-degree counterclockwise rotation** around the origin.

The general rule for a 90-degree counterclockwise rotation around the origin is:
\[
(x, y) \rightarrow (-y, x)
\]

Thus, the transformation rule that maps the pre-image \( A \) to the image \( B \) is:
\[
(x, y) \rightarrow (-y, x)
\]

Would you like further explanation on this transformation or details on how the rotation was derived?

Here are some related questions to expand your understanding:
1. How can we differentiate between a reflection and a rotation transformation?
2. What is the transformation rule for a 90-degree clockwise rotation?
3. How do we perform translations on a coordinate plane?
4. Can a combination of transformations (rotation + translation) be used to map A to B?
5. How would the transformation rule change if we rotated 180 degrees?

**Tip**: When solving transformations, always check both the orientation and the distance between points to accurately determine the type of transformation applied.

Complete the description of the transformation that maps the pre-image A to the image B. The options provided are numbers and symbols to form the transformation rule.

This question involves mapping the pre-image A to image B using a transformation in coordinate geometry. The solution involves recognizing a 90-degree counterclockwise rotation around the origin, following the transformation rule (x, y) → (-y, x). Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation