Kirk Best
06/05/2023 · Junior High School
Find the composition of transformations that map ABCD to EHGF. Reflect over the [?]-axis, then translate ( \( x+[1, y+[ \) ]). Note: Enter \( x \) or \( y \) for axis.
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To find the composition of transformations that map quadrilateral ABCD to quadrilateral EHGF, we can follow the steps outlined in your question.
1. **Reflect over the y-axis**: This transformation will change the x-coordinates of the points in ABCD. If a point \( (x, y) \) is reflected over the y-axis, it becomes \( (-x, y) \).
2. **Translate**: The translation you provided is \( (x + 1, y + 1) \). This means that after reflecting the points, we will add 1 to the x-coordinate and 1 to the y-coordinate of each point.
Putting it all together, the composition of transformations is as follows:
1. **Reflect over the y-axis**: \( (x, y) \rightarrow (-x, y) \)
2. **Translate**: \( (-x, y) \rightarrow (-x + 1, y + 1) \)
So, the complete transformation that maps ABCD to EHGF is:
- Reflect over the **y-axis**
- Then translate by \( (x + 1, y + 1) \)
Thus, the answer is:
- Reflect over the **y-axis**
- Then translate \( (x + 1, y + 1) \)
Quick Answer
Reflect over the y-axis, then translate \( (x + 1, y + 1) \)
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