https://r2.erweima.ai/mathbot/image/1726711400350mjy2bd3x.jpg

The problem asks to perform a sequence of transformations on **Figure A**:

1. **Translation**: Move **Figure A** 6 units down to form **Figure D**.
2. **Rotation**: Rotate **Figure D** by 90° clockwise around the origin to form **Figure E**.
3. **Question**: Does this sequence of transformations map **Figure A** onto **Figure C**?

### Step 1: Translation of Figure A to Form Figure D
- Looking at the graph, we first need to translate **Figure A** 6 units down. 
- The coordinates of **Figure A**’s vertices (corners of the shape) need to be adjusted by subtracting 6 from their **y-coordinates**.

If **Figure A** has vertices at points:
- (2, 6)
- (2, 4)
- (4, 4)
- (4, 2)

After translating 6 units down, the new coordinates (for **Figure D**) will be:
- (2, 0)
- (2, -2)
- (4, -2)
- (4, -4)

### Step 2: Rotation of Figure D to Form Figure E
- Next, we rotate **Figure D** 90° clockwise around the origin. When rotating 90° clockwise, the transformation of any point \((x, y)\) becomes \((y, -x)\).

Applying this to the coordinates of **Figure D**:
- (2, 0) → (0, -2)
- (2, -2) → (-2, -2)
- (4, -2) → (-2, -4)
- (4, -4) → (-4, -4)

These new coordinates represent **Figure E** after rotation.

### Step 3: Comparison with Figure C
To check if **Figure E** matches **Figure C**, we would need to visually compare the positions of the vertices. If the vertices of **Figure E** coincide with those of **Figure C**, then the sequence of transformations successfully maps **Figure A** onto **Figure C**. 

Please let me know if you would like further explanation on the transformations or if you have any specific questions! 

---

Here are 5 relative questions to expand understanding:
1. What is the rule for a 90° clockwise rotation around the origin?
2. How do you apply a translation on a coordinate plane?
3. What is the effect of translating by different directions (up/down/left/right)?
4. How do reflections differ from rotations and translations?
5. Can a sequence of transformations ever return a figure to its original position?

**Tip**: When performing a rotation, always remember that each point's new position is based on both the direction of rotation and its distance from the origin.

Translate figure A from the Example 6 units down to form figure D. Then rotate figure D 90° clockwise around the origin to form figure E. Does this sequence of transformations map figure A onto figure C? Explain.

Learn how to perform a sequence of geometric transformations on a figure. This problem involves translating a figure down and then rotating it 90° clockwise around the origin. Check if the transformations map the figure to the desired target. 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