figures D and E are congruent. Figure D, with coordinates (1,2),(1,3),(3,5), and (4,1), is rotated 90 degrees clockwise about the origin and than reflected over the y-axis to transform onto figure E. what are the coordinates of figure E?

To find the coordinates of figure E, we need to apply two transformations to figure D: a 90-degree clockwise rotation about the origin, followed by a reflection over the y-axis.

Let's go step by step:

### Step 1: 90-degree clockwise rotation about the origin
When a point \((x, y)\) is rotated 90 degrees clockwise about the origin, its new coordinates become \((y, -x)\).

Let’s apply this transformation to each of the points of figure D:

- \((1, 2) \rightarrow (2, -1)\)
- \((1, 3) \rightarrow (3, -1)\)
- \((3, 5) \rightarrow (5, -3)\)
- \((4, 1) \rightarrow (1, -4)\)

### Step 2: Reflection over the y-axis
When a point \((x, y)\) is reflected over the y-axis, its new coordinates become \((-x, y)\).

Let’s apply this transformation to the points we obtained from the rotation:

- \((2, -1) \rightarrow (-2, -1)\)
- \((3, -1) \rightarrow (-3, -1)\)
- \((5, -3) \rightarrow (-5, -3)\)
- \((1, -4) \rightarrow (-1, -4)\)

### Final coordinates of figure E:
Thus, the coordinates of figure E are:
- \((-2, -1)\)
- \((-3, -1)\)
- \((-5, -3)\)
- \((-1, -4)\)

Would you like more details or have any questions?

Here are 5 related questions:
1. What are the coordinates if figure D were reflected over the x-axis instead of the y-axis?
2. How would the coordinates change if the rotation was counterclockwise instead of clockwise?
3. Can a translation be combined with rotation and reflection to form a new transformation?
4. How do you determine if two figures are congruent through transformations?
5. What happens if you apply two reflections to a figure—one over the x-axis and one over the y-axis?

**Tip:** When rotating figures, it's helpful to visualize how the points move quadrant by quadrant to avoid confusion with sign changes.

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

Learn how to transform figure D into figure E using a 90-degree clockwise rotation about the origin and a reflection over the y-axis. This step-by-step guide covers key concepts in coordinate geometry, including transformations and congruence. Suitable for students in Grades 8-10.

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