Question

Use the coordinates to answer the question.
Point F: (-5, 5)
Point U: (-1, 4)
Point N: (-3, 0)
x = -1

For Triangle FUN, x = -1. What are the coordinates for F' after a reflection?

Answer 1

To find the coordinates of point F' after reflecting point F across the line \( x = -1 \), we need to determine how far point F is from the line and then find the new coordinates of F' based on that reflection.

1. **Identify the x-coordinate of point F**:
- Point F has coordinates (-5, 5).

2. **Find the distance from F to the line \( x = -1 \)**:
- The x-coordinate of F is -5. The distance from -5 to -1 is:
\[
|-5 - (-1)| = |-5 + 1| = |-4| = 4
\]

3. **Reflect F across the line \( x = -1 \)**:
- To reflect point F, we will move it 4 units to the right (toward the line \( x = -1 \)). The new x-coordinate will be:
\[
-1 + 4 = 3
\]
- The y-coordinate remains the same during reflection, so it stays 5.

4. **Write the coordinates for F'**:
- The coordinates of point F' after reflection will therefore be:
\[
F' = (3, 5)
\]

Thus, the coordinates for F' after the reflection across the line \( x = -1 \) are \((3, 5)\).