To reflect a point across a vertical line (in this case, \( x = -1 \)), we can follow these steps:
-
Identify the original point: The coordinates for point \( F \) are given as \( (-5, 5) \).
-
Determine the distance from the point to the line of reflection: The line of reflection is \( x = -1 \). The distance from \( F \) to the line can be calculated as follows: \[ \text{Distance} = -1 - (-5) = -1 + 5 = 4 \] This means point \( F \) is 4 units to the left of the line \( x = -1 \).
-
Reflect the point across the line: To find the reflected point \( F' \), we need to move the same distance to the right of the line. Therefore, we add 4 units to the x-coordinate of the line of reflection: \[ x' = -1 + 4 = 3 \] The y-coordinate remains the same during a vertical reflection, so: \[ y' = 5 \]
-
Final coordinates: The coordinates for the reflected point \( F' \) are \( (3, 5) \).
Thus, after a reflection across the line \( x = -1 \), the coordinates for point \( F' \) are \( (3, 5) \).