Triangle FUN is reflected over the line x = -1.

Question

What are the coordinates of N' after the reflection?

Answer 1

To reflect a point across a vertical line (in this case, the line \( x = -1 \)), you need to follow these steps:

1. Determine the x-coordinate of the original point N.
2. Find the distance from the point N to the line of reflection (x = -1).
3. Move the same distance on the opposite side of the line to find the new x-coordinate of N'.

Let's assume the original coordinates of point N are given by \( (x_N, y_N) \).

Steps to Reflect:

1. Calculate the distance from point N to the line x = -1: \[ \text{Distance} = x_N - (-1) = x_N + 1 \]

2. Determine the new x-coordinate after reflection: \[ x_{N'} = -1 - (x_N + 1) = -1 - x_N - 1 = -x_N - 2 \]

3. The y-coordinate remains the same: \[ y_{N'} = y_N \]

Therefore, the new coordinates of point N' after the reflection are: \[ (-x_N - 2, y_N) \]

If you provide the specific coordinates of point N, I can give you the exact coordinates of N' after the reflection.