https://file.aiquickdraw.com/mathbot/file/1727398053858pm13d1bl.jpg

The image shows a pair of parallelograms, \( ABCD \) and \( A'B'C'D' \), graphed on a coordinate plane. Below the graph, the question asks: **"Which sequences of transformations map ABCD onto A'B'C'D'? Select all that apply."**

One option is already checked:
- A rotation of 180° around the origin, followed by a translation right 3 units and up 2 units.

Other options presented include translations, reflections, and rotations. The goal is to determine which sequences accurately map \( ABCD \) to \( A'B'C'D' \).

### Let's analyze the transformations:
1. **Rotation 180° around the origin:**
   - This would flip the parallelogram about the origin, reversing its orientation but keeping the size and shape intact. Visually, after a 180° rotation, the parallelogram would be in a similar orientation to \( A'B'C'D' \) but would require a translation to match it.

2. **Translation (right 3 units and up 2 units):**
   - After the 180° rotation, moving the image right 3 units and up 2 units would likely align it with \( A'B'C'D' \), confirming this option as correct (which is already selected).

3. **Other options:**
   - A translation followed by another rotation: This would not directly map the two figures.
   - Reflection and translation sequences: These would mirror the figure across an axis and may not correctly map to \( A'B'C'D' \) without distorting the orientation.

Thus, the first option is correct based on the provided information and visual analysis.

Do you have any questions, or would you like more details? Here are 5 related questions that might interest you:

1. What are the properties of a 180° rotation around the origin in the coordinate plane?
2. How do translations affect geometric shapes on a coordinate plane?
3. What is the difference between rotation and reflection in transformations?
4. How do you determine the sequence of transformations that map one figure onto another?
5. What are some common strategies for solving transformation problems in geometry?

**Tip:** When applying transformations, always consider both the orientation and the position of the shape to ensure the transformation sequence is accurate.

Which sequences of transformations map ABCD onto A'B'C'D'? Select all that apply.

Analyze sequences of transformations such as rotations, translations, and reflections that map parallelogram ABCD onto A'B'C'D' using key geometric principles. Suitable for 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