https://file.aiquickdraw.com/mathbot/file/17308670002895l6nzyix.jpg

To reflect each point over the line \( x = 1 \), we'll follow these steps:

1. Identify each original point’s coordinates.
2. Calculate the reflection of each point over the line \( x = 1 \).

The rule for reflecting a point \( (x, y) \) over a vertical line \( x = k \) is that the reflected point’s \( x \)-coordinate will be \( 2k - x \), while the \( y \)-coordinate remains unchanged.

Let's proceed with each point:

### Original Coordinates
- **S** appears to be at \( (-6, -3) \).
- **T** appears to be at \( (-3, 1) \).
- **U** appears to be at \( (-1, 4) \).
- **V** appears to be at \( (2, 2) \).

### Reflected Coordinates
Since we are reflecting over the line \( x = 1 \):
- For **S**: \( S' = (2 \times 1 - (-6), -3) = (2 + 6, -3) = (8, -3) \)
- For **T**: \( T' = (2 \times 1 - (-3), 1) = (2 + 3, 1) = (5, 1) \)
- For **U**: \( U' = (2 \times 1 - (-1), 4) = (2 + 1, 4) = (3, 4) \)
- For **V**: \( V' = (2 \times 1 - 2, 2) = (2 - 2, 2) = (0, 2) \)

### Reflected Coordinates Summary
- \( S' = (8, -3) \)
- \( T' = (5, 1) \)
- \( U' = (3, 4) \)
- \( V' = (0, 2) \)

Please confirm if you'd like more details on the reflection process or have any further questions.

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**Here are some additional questions for further exploration:**

1. What would the coordinates be if we reflected the points over a different line, such as \( x = -1 \)?
2. How can you find the reflection of a point over a horizontal line, like \( y = 0 \)?
3. If we translated the figure 3 units up after reflecting, what would the new coordinates be?
4. How does the reflection over the line \( x = 1 \) differ from a reflection over the line \( x = 0 \)?
5. How can reflections be used in solving geometric problems involving symmetry?

**Tip:** When reflecting over a line, focus on how far each point is from the line to make it easy to calculate the reflected point's new coordinates.

Write the coordinates of the vertices after a reflection over the line x = 1 for points S, T, U, and V.

Learn how to reflect points over a vertical line in coordinate geometry. This example reflects points S, T, U, and V over the line x = 1, demonstrating the formula (2k - x, y). Suitable for Grades 8-10.

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