Asked by Aaliyah
Triangle XYZ is reflected over a horizontal line of reflection to create triangle X’Y’Z’. What are the coordinates of vertex X’
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine the coordinates of vertex \( X' \) after triangle \( XYZ \) is reflected over a horizontal line, we first need to know the coordinates of vertex \( X \) and the y-coordinate of the line of reflection.
Assuming:
- The coordinates of vertex \( X \) are \( (x, y) \).
- The equation of the horizontal line of reflection is \( y = k \) (where \( k \) is the y-coordinate of the line).
The reflection of a point \( (x, y) \) over the line \( y = k \) is found by calculating the new y-coordinate as follows:
1. Find the vertical distance from point \( X \) to the line of reflection: \( d = y - k \).
2. Since reflection will place the point the same distance on the opposite side of the line, the new y-coordinate \( y' \) will be:
\[
y' = k - d = k - (y - k) = 2k - y
\]
3. The x-coordinate remains unchanged.
Thus, the coordinates of vertex \( X' \) after reflection will be:
\[
X' = (x, 2k - y)
\]
If you provide the coordinates of vertex \( X \) and the line of reflection, I can give you the specific coordinates of \( X' \).
Assuming:
- The coordinates of vertex \( X \) are \( (x, y) \).
- The equation of the horizontal line of reflection is \( y = k \) (where \( k \) is the y-coordinate of the line).
The reflection of a point \( (x, y) \) over the line \( y = k \) is found by calculating the new y-coordinate as follows:
1. Find the vertical distance from point \( X \) to the line of reflection: \( d = y - k \).
2. Since reflection will place the point the same distance on the opposite side of the line, the new y-coordinate \( y' \) will be:
\[
y' = k - d = k - (y - k) = 2k - y
\]
3. The x-coordinate remains unchanged.
Thus, the coordinates of vertex \( X' \) after reflection will be:
\[
X' = (x, 2k - y)
\]
If you provide the coordinates of vertex \( X \) and the line of reflection, I can give you the specific coordinates of \( X' \).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.