What are the coordinates of Y' after a reflection across y = 1?

axis of reflection: y = 1
Triangle points
Point Y: (4, 3)
Point X: (1, -1)
Point Z: (6, 0)

A. Y' (-2, 3)
B. Y' (4, -1)
C. Y' (-2, -1)
D. Y' (4, 5)

1 answer

To find the coordinates of point Y' after reflecting point Y across the line \( y = 1 \), we need to determine the distance of point Y from the line of reflection and then reflect it across that line.

  1. Identify the coordinates of point Y: \( Y(4, 3) \).

  2. Calculate the distance from point Y to the line \( y = 1 \): The y-coordinate of Y is 3 and the y-coordinate of the line of reflection is 1. The distance from Y to the line is: \[ 3 - 1 = 2 \]

  3. Reflect point Y across the line \( y = 1 \): To reflect Y across the line, we subtract the distance from the line: \[ Y' = (4, 1 - 2) = (4, -1) \]

So, the reflected point Y' is at the coordinates \( (4, -1) \).

Therefore, the correct answer is B. Y' (4, -1).