Question
This image is a coordinate plane showing a triangle and an axis of reflection. Here are the details: Points and Triangle: Point X at (1, -1) Point Y at (4, 3) Point Z at (6, 0) These points form a triangle connected by orange lines. Axis of Reflection: There is a dotted blue line labeled "axis of reflection" along the line y = 1. Axes: The x-axis ranges from -7 to 7. The y-axis ranges from -7 to 7.
What are the coordinates of Y′
after a reflection across y=1
?
(1 point)
Responses
Y′(−2,3)
upper Y prime left parenthesis negative 2 comma 3 right parenthesis
Y′(−2,−1)
upper Y prime left parenthesis negative 2 comma negative 1 right parenthesis
Y′(4,−1)
upper Y prime left parenthesis 4 comma negative 1 right parenthesis
Y′(4,5)
What are the coordinates of Y′
after a reflection across y=1
?
(1 point)
Responses
Y′(−2,3)
upper Y prime left parenthesis negative 2 comma 3 right parenthesis
Y′(−2,−1)
upper Y prime left parenthesis negative 2 comma negative 1 right parenthesis
Y′(4,−1)
upper Y prime left parenthesis 4 comma negative 1 right parenthesis
Y′(4,5)
Answers
GPT-4o mini
To find the coordinates of \( Y' \) (the reflection of point \( Y \)) after reflecting across the line \( y = 1 \):
1. Start with the coordinates of point \( Y \):
\[
Y(4, 3)
\]
2. To reflect a point across the line \( y = k \), you can use the formula:
\[
Y' = (x, k - (y - k))
\]
Here, \( k \) represents the y-value of the line of reflection, which is 1.
3. Applying this to point \( Y \):
\[
Y' = (4, 1 - (3 - 1))
\]
Simplifying this:
\[
Y' = (4, 1 - 2) = (4, -1)
\]
Thus, the coordinates of \( Y' \) after reflection across the line \( y = 1 \) are \( (4, -1) \).
Therefore, the correct response is:
**Y′(4,−1)**
1. Start with the coordinates of point \( Y \):
\[
Y(4, 3)
\]
2. To reflect a point across the line \( y = k \), you can use the formula:
\[
Y' = (x, k - (y - k))
\]
Here, \( k \) represents the y-value of the line of reflection, which is 1.
3. Applying this to point \( Y \):
\[
Y' = (4, 1 - (3 - 1))
\]
Simplifying this:
\[
Y' = (4, 1 - 2) = (4, -1)
\]
Thus, the coordinates of \( Y' \) after reflection across the line \( y = 1 \) are \( (4, -1) \).
Therefore, the correct response is:
**Y′(4,−1)**