Question

Triangle FUN is reflected across x=−1 . What are the coordinates of N′ after the reflection? (1 point) Responses (3, 0) (3, 0) (0,1) (0,1) (3, 5) (3, 5) (1, 0)

Answer 1

what the answer to this

Answer 2

To find the coordinates of point N' after reflecting point N across the line \( x = -1 \), we can follow these steps:

1. Identify the original coordinates of point N. (Since you haven't provided the coordinates of point N, let's denote them as \( (x_N, y_N) \).)

2. The line \( x = -1 \) is a vertical line. When reflecting across this line, the x-coordinate of a point will change while the y-coordinate will remain the same.

3. To calculate the reflected x-coordinate:
- Measure the distance from the original x-coordinate to the line \( x = -1 \).
- The reflection will be the same distance on the other side of the line.

The formula for reflecting a point \( (x, y) \) across the line \( x = -1 \) is:
- New x-coordinate \( x' = -1 - (x + 1) = -2 - x \)
- Y-coordinate stays the same \( y' = y \)

If we had the original coordinates of point N, we could simply apply this method.

For example, let's say point N has coordinates \( (3, 0) \):
- The distance from the point \( (3, 0) \) to the line \( x = -1 \) is \( 3 - (-1) = 4 \).
- The reflected point \( N' \) will be at \( -1 - 4 = -5\), so the coordinates of \( N' \) would be \( (-5, 0) \).

Since you provided a list of possible responses, please provide the coordinates for point N so that I can compute the correct reflected coordinates for N'.

Answer 3

To identify the answer for the reflection of point \( N \) across the line \( x = -1 \), we first need the original coordinates of point \( N \). From the options you provided, it looks like the possible coordinate responses for the reflected point are:

1. (3, 0)
2. (0, 1)
3. (3, 5)
4. (1, 0)

Since we've concluded that we must reflect across the line \( x = -1 \), I will demonstrate how to determine if any of these points could be the result of reflection.

For a point \( (x, y) \) to be reflected across the line \( x = -1 \):
- The x-coordinate of the reflected point \( N' \) will be calculated as:
\[
x' = -1 - (x + 1) = -2 - x
\]

Let's analyze each option to determine which might correspond to a reflection and find the original point N.

1. **(3, 0)**
- \( x' = 3 \)
- So, original \( x = -2 - 3 = -5 \) → Original point \( (-5, 0) \)

2. **(0, 1)**
- \( x' = 0 \)
- So, original \( x = -2 - 0 = -2 \) → Original point \( (-2, 1) \)

3. **(3, 5)**
- \( x' = 3 \)
- So, original \( x = -2 - 3 = -5 \) → Original point \( (-5, 5) \)

4. **(1, 0)**
- \( x' = 1 \)
- So, original \( x = -2 - 1 = -3 \) → Original point \( (-3, 0) \)

Based on this evaluation, let's summarize:
- For any point \( (3, 0) \) or \( (3, 5) \), the reflection would land on (3, 0) which doesn't result in a change of coordinates, meaning initially it isn't the correct reflection.
- The reflected point (0, 1) and (1, 0) could potentially result after reflecting from positions -2 or -3 respectively.

Given your question, none of these provided options directly indicate a clear reflection from a specific original point unless we assume an unknown N for them. However, if point N were specifically said to be one of these points, then evaluating and reflecting based on x-coordinates would clarify the outputs correctly.

If you meant to provide the coordinates of point N, please let me know, and I can provide better-guided results! If you're confirming to align with specific outputs from a direct reflection, let me know what that might be.