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It looks like you've uploaded an image that includes questions involving transformations, dilation, reflection, and coordinate geometry. Based on the text in the image, I can help walk through the solution for the questions visible.

The key question asks for the coordinates of △ABC after several transformations, including:

1. Reflection over the y-axis.
2. Dilation by a scale factor of 2 about the point \(E(-3, 5)\).

To solve these steps, let’s break them down:

### 1. Reflection over the y-axis:
The general rule for reflecting over the y-axis is:
- \( (x, y) \rightarrow (-x, y) \).

Let’s apply this rule to the preimage coordinates:

- \( A(2, 1) \rightarrow A'(-2, 1) \)
- \( B(2, 3) \rightarrow B'(-2, 3) \)
- \( C(1, -1) \rightarrow C'(-1, -1) \)

### 2. Dilation about the point \(E(-3, 5)\) with a scale factor of 2:
The formula for dilation is:
- \( (x, y) \rightarrow (x_{new}, y_{new}) = (x_s, y_s) + k \cdot ((x, y) - (x_s, y_s)) \),
  where \( (x_s, y_s) \) is the center of dilation, and \( k \) is the scale factor.

Using the center \( E(-3, 5) \) and scale factor \( k = 2 \), we dilate each point:

- For \( A'(-2, 1) \):
  \[
  A'' = (-3, 5) + 2 \cdot ((-2, 1) - (-3, 5)) = (-3, 5) + 2 \cdot (1, -4) = (-3, 5) + (2, -8) = (-1, -3)
  \]
- For \( B'(-2, 3) \):
  \[
  B'' = (-3, 5) + 2 \cdot ((-2, 3) - (-3, 5)) = (-3, 5) + 2 \cdot (1, -2) = (-3, 5) + (2, -4) = (-1, 1)
  \]
- For \( C'(-1, -1) \):
  \[
  C'' = (-3, 5) + 2 \cdot ((-1, -1) - (-3, 5)) = (-3, 5) + 2 \cdot (2, -6) = (-3, 5) + (4, -12) = (1, -7)
  \]

### Final Coordinates:
- \( A''(-1, -3) \)
- \( B''(-1, 1) \)
- \( C''(1, -7) \)

These are the coordinates of △ABC after the dilation and reflection.

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Let me know if you'd like a more detailed explanation of each step or have questions. Here are some related questions to expand on this topic:

1. What happens when you reflect a point over the x-axis instead of the y-axis?
2. How does changing the scale factor of dilation affect the size of the image?
3. What is the effect of translating a figure by different units along the x- and y-axis?
4. How can you determine the center of dilation if it’s not given?
5. What are the different types of transformations in geometry?

**Tip:** Always double-check the transformation rules for each type of motion (reflection, translation, dilation) to ensure accuracy.

The preimage of triangle ABC has coordinates A(2, 1), B(2, 3), and C(1, -1). Triangle ABC is then reflected over the y-axis and dilated about the point E(-3, 5) by a scale factor of 2. What are the final image coordinates of triangle ABC?

Solve a transformation problem involving triangle ABC, reflected over the y-axis and then dilated by a scale factor of 2 about the point E(-3, 5). Learn the process of finding the final image coordinates step-by-step.

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