Question
Triangle XYZ is reflected over a horizontal line of reflection to create triangle X′Y′Z′ . What are the coordinates of vertex X′ ? (1 point) Responses (−2,−2) left parenthesis negative 2 comma negative 2 right parenthesis (3,−9) left parenthesis 3 comma negative 9 right parenthesis (−3,−7) left parenthesis negative 3 comma negative 7 right parenthesis (−3,−9)
Answers
GPT-4o mini
To determine the coordinates of vertex \( X' \) after reflecting triangle \( XYZ \) over a horizontal line of reflection, we need to know the original coordinates of vertex \( X \) and the line of reflection.
Let's denote the coordinates of vertex \( X \) as \( (x, y) \). When reflecting over a horizontal line \( y = k \), the \( y \)-coordinate of the reflected point \( X' \) will change according to the formula:
\[
y' = 2k - y
\]
The \( x \)-coordinate remains the same:
\[
x' = x
\]
Without knowing the specific coordinates of vertex \( X \) or the line of reflection, we cannot definitively calculate the new coordinates of \( X' \).
If you have more information, such as the coordinates of point \( X \) and the equation of the line of reflection, please share so I can assist you further! Otherwise, with the responses provided, it seems necessary to deduce the possible coordinates based on typical triangular reflections.
Here are the possible listed responses, from which one can choose the correct one after determining the original coordinates and the line of reflection:
1. \( (-2, -2) \)
2. \( (3, -9) \)
3. \( (-3, -7) \)
4. \( (-3, -9) \)
Please provide additional details if available!
Let's denote the coordinates of vertex \( X \) as \( (x, y) \). When reflecting over a horizontal line \( y = k \), the \( y \)-coordinate of the reflected point \( X' \) will change according to the formula:
\[
y' = 2k - y
\]
The \( x \)-coordinate remains the same:
\[
x' = x
\]
Without knowing the specific coordinates of vertex \( X \) or the line of reflection, we cannot definitively calculate the new coordinates of \( X' \).
If you have more information, such as the coordinates of point \( X \) and the equation of the line of reflection, please share so I can assist you further! Otherwise, with the responses provided, it seems necessary to deduce the possible coordinates based on typical triangular reflections.
Here are the possible listed responses, from which one can choose the correct one after determining the original coordinates and the line of reflection:
1. \( (-2, -2) \)
2. \( (3, -9) \)
3. \( (-3, -7) \)
4. \( (-3, -9) \)
Please provide additional details if available!