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.