Question

for triangle FUN (-5,5), (-3,0),& (-1,4), x = -1. what are the coordinates for F' after a reflection?

Answer 1

To reflect a point across a vertical line (in this case, \( x = -1 \)), we can follow these steps:

1. **Identify the original point**:
The coordinates for point \( F \) are given as \( (-5, 5) \).

2. **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 \( x = -1 \).

3. **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:
\[
y' = 5
\]

4. **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 \( (3, 5) \).