https://file.aiquickdraw.com/mathbot/file/1727361025846fb2ssif7.jpg

In the given problem, the pre-image \( GHJK \) is being transformed into the final image \( G'H'J'K' \). Based on the image and the provided options, we are tasked with identifying the first transformation (either a rotation or reflection) and then a translation.

### Observations:
1. **Pre-image (GHJK)** is positioned horizontally, while the final image \( G'H'J'K' \) is vertically oriented.
2. **Final Image Position**: The shape has been rotated and translated.
3. **Rotation Analysis**: The shape has been rotated counterclockwise from its original position. Given the choices, the shape appears to be rotated by 90° counterclockwise around point \( K \), as it preserves the relative orientation of points after the rotation.

### Translation:
After the rotation, the image needs to be translated to match the position of \( G'H'J'K' \), which is a translation to the right (as described in the prompt).

### Solution:
- The **first transformation** is a **90° counterclockwise rotation about point \( K \)**.
- The second transformation is a **translation to the right**.

Would you like further clarification on any step, or additional questions to explore this concept?

---

Here are five related questions:
1. What would happen if we applied a 270° counterclockwise rotation instead?
2. How do you determine the center of rotation for any transformation?
3. What is the general formula for finding the coordinates of a point after rotation?
4. How would this problem change if the translation were to the left instead of the right?
5. Can the order of transformations affect the final result? If so, how?

**Tip:** When dealing with transformations, always visualize how each step (rotation, reflection, translation) alters the position and orientation of the shape.

A composition of transformations maps pre-image GHJK to the final image G'H'J'K'. The first transformation is a rotation, and the second is a translation to the right.

Explore how a quadrilateral GHJK is transformed through a 90° counterclockwise rotation about point K and a translation to the right. Understand key geometric concepts like rotations and translations, 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