Use the coordinates to answer the question.

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 \((3, 5)\).