Select the correct answer from each drop-down menu.
Graph of 2 polygons. Polygon 1 at A (minus 6, 6), B (minus 4, 6), C (minus 4, 4), D (minus 6, 2) in quadrant 2. Polygon 2, A prime (minus 6, minus 6), B prime (minus 6, minus 4), C prime (minus 4, minus 4), D prime (minus 2, minus 6) in quadrant 4.

Polygon ABCD goes through a sequence of rigid transformations to form polygon A′B′C′D′. The sequence of transformations involved is a reflection across the 
, followed by a reflection across the line 
.

The given polygons suggest a sequence of rigid transformations.

1. **Step 1**: Polygon 1 (ABCD) is reflected across the **x-axis**. This is because the coordinates of Polygon 1 in Quadrant II (negative x, positive y) are transformed to Quadrant IV (negative x, negative y), indicating a reflection over the x-axis.

2. **Step 2**: The second reflection results in the transformation of the points further within Quadrant IV. A reflection across the **y-axis** would not produce the observed coordinates of Polygon 2 (A'B'C'D'), but instead, a reflection across the line **y = -x** achieves this. The points are mirrored in such a way that the new coordinates match.

Thus, the correct sequence of transformations is:
- A reflection across the **x-axis**, followed by
- A reflection across the line **y = -x**.

Does that answer help clarify the problem for you? Here are five related questions:

1. What is the definition of a rigid transformation in geometry?
2. Can two reflections across different axes ever be equivalent to a single transformation? If so, when?
3. How can you determine which axis or line a polygon was reflected over, just from its coordinates?
4. What happens to the coordinates of a point after reflecting it over the line y = x?
5. How do reflections affect the orientation of a shape?

**Tip**: When reflecting a point across the x-axis, its y-coordinate changes sign while the x-coordinate remains the same.

Select the correct answer from each drop-down menu. Graph of 2 polygons. Polygon 1 at A (minus 6, 6), B (minus 4, 6), C (minus 4, 4), D (minus 6, 2) in quadrant 2. Polygon 2, A prime (minus 6, minus 6), B prime (minus 6, minus 4), C prime (minus 4, minus 4), D prime (minus 2, minus 6) in quadrant 4. Polygon ABCD goes through a sequence of rigid transformations to form polygon A′B′C′D′. The sequence of transformations involved is a reflection across the , followed by a reflection across the line .

Understand how to transform polygon ABCD through a sequence of reflections over the x-axis and the line y = -x. This detailed explanation covers rigid transformations, reflections, and coordinate geometry 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