Question
point y (4,3) is reflected across horizontal line y = 1. what will be the coordinates of Y'
Answers
GPT-4o mini
To reflect the point \( Y(4, 3) \) across the horizontal line \( y = 1 \), follow these steps:
1. Determine the vertical distance from the point \( Y \) to the line \( y = 1 \). The y-coordinate of point \( Y \) is 3, so the distance to \( y = 1 \) is \( 3 - 1 = 2 \).
2. Since the reflection across the line means moving the same distance on the opposite side of the line, you subtract this distance from the line's y-coordinate:
\[
y' = 1 - 2 = -1
\]
3. The x-coordinate remains unchanged during reflection across a horizontal line. Thus, the x-coordinate of \( Y' \) remains 4.
Putting this all together, the coordinates of the reflected point \( Y' \) will be:
\[
Y'(4, -1)
\]
1. Determine the vertical distance from the point \( Y \) to the line \( y = 1 \). The y-coordinate of point \( Y \) is 3, so the distance to \( y = 1 \) is \( 3 - 1 = 2 \).
2. Since the reflection across the line means moving the same distance on the opposite side of the line, you subtract this distance from the line's y-coordinate:
\[
y' = 1 - 2 = -1
\]
3. The x-coordinate remains unchanged during reflection across a horizontal line. Thus, the x-coordinate of \( Y' \) remains 4.
Putting this all together, the coordinates of the reflected point \( Y' \) will be:
\[
Y'(4, -1)
\]