Figures ABCD and EFGH are congruent. Figure ABCD, with coordinates A(1, 2), B(1, 3), C(3, 5), and D(4, 1), is rotated  90°  clockwise about the origin and then reflected over the y-axis to transform onto figure EFGH. What are the coordinates of figure EFGH? Enter the answers.

To solve this problem, we'll apply the given transformations step by step:

### Step 1: Rotate Figure ABCD 90° Clockwise
For a 90° clockwise rotation about the origin, the transformation for each point \((x, y)\) is:
\[
(x', y') = (y, -x)
\]

Let’s apply this transformation to each vertex of figure ABCD:

- **A(1, 2)**:  
\[
A' = (2, -1)
\]
- **B(1, 3)**:  
\[
B' = (3, -1)
\]
- **C(3, 5)**:  
\[
C' = (5, -3)
\]
- **D(4, 1)**:  
\[
D' = (1, -4)
\]

So after the 90° clockwise rotation, the new coordinates of figure ABCD are:  
\[
A'(2, -1), B'(3, -1), C'(5, -3), D'(1, -4)
\]

### Step 2: Reflect the Rotated Figure over the y-axis
For a reflection over the y-axis, the transformation for each point \((x', y')\) is:
\[
(x'', y'') = (-x', y')
\]

Now, apply this transformation to each rotated point:

- **A'(2, -1)**:  
\[
A'' = (-2, -1)
\]
- **B'(3, -1)**:  
\[
B'' = (-3, -1)
\]
- **C'(5, -3)**:  
\[
C'' = (-5, -3)
\]
- **D'(1, -4)**:  
\[
D'' = (-1, -4)
\]

### Final Coordinates of Figure EFGH
The coordinates of figure EFGH after the transformations are:
\[
E(-2, -1), F(-3, -1), G(-5, -3), H(-1, -4)
\]

Thus, the coordinates of figure EFGH are:
- \(E(-2, -1)\)
- \(F(-3, -1)\)
- \(G(-5, -3)\)
- \(H(-1, -4)\)

Do you have any questions or want more details on any of the steps?

Here are five related questions to think about:
1. What are the formulas for 90° and 180° counterclockwise rotations about the origin?
2. How would the coordinates change if the reflection were over the x-axis instead of the y-axis?
3. How does a 270° clockwise rotation affect the points compared to a 90° rotation?
4. What is the result of applying both a rotation and a reflection in reverse order?
5. How would this process change if figure ABCD were scaled before the transformations?

**Tip:** When rotating points, always double-check the sign changes in the coordinates to ensure accuracy.

Figures ABCD and EFGH are congruent. Figure ABCD, with coordinates A(1, 2), B(1, 3), C(3, 5), and D(4, 1), is rotated 90° clockwise about the origin and then reflected over the y-axis to transform onto figure EFGH. What are the coordinates of figure EFGH?

Learn how to transform figure ABCD through a 90° clockwise rotation about the origin followed by a reflection over the y-axis. This detailed solution covers geometric transformations and provides the coordinates of the resulting figure EFGH. Suitable for students in Grades 8-10.

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