Question

Point Y(4,3)
is reflected across horizontal line y=1
. What will be the coordinates of Y′
?

Answer 1

To reflect the point \( Y(4, 3) \) across the horizontal line \( y = 1 \), we need to determine the distance of point \( Y \) from the line and then find the point at the same distance on the opposite side.

1. **Find the vertical distance from point \( Y \) to the line \( y = 1 \)**:

The \( y \)-coordinate of point \( Y \) is \( 3 \). The line is at \( y = 1 \).

The distance from \( Y \) to the line is:
\[
3 - 1 = 2
\]

2. **Reflect over the line by going the same distance below the line**:
To find the reflected point \( Y' \), we subtract the distance from the line:
\[
y' = 1 - 2 = -1
\]

3. **The \( x \)-coordinate remains the same** (since it is a horizontal reflection):
Therefore, the coordinates of point \( Y' \) will be:
\[
Y' = (4, -1)
\]

So the coordinates of \( Y' \) after reflection across the line \( y = 1 \) are \( (4, -1) \).