Question

Triangle XYZ is reflected over a horizontal line of reflection to create triangle X’Y’Z’. What are the coordinates of vertex X’

Answer 1

To determine the coordinates of vertex \( X' \) after triangle \( XYZ \) is reflected over a horizontal line, we first need to know the coordinates of vertex \( X \) and the y-coordinate of the line of reflection.

Assuming:

- The coordinates of vertex \( X \) are \( (x, y) \).
- The equation of the horizontal line of reflection is \( y = k \) (where \( k \) is the y-coordinate of the line).

The reflection of a point \( (x, y) \) over the line \( y = k \) is found by calculating the new y-coordinate as follows:

1. Find the vertical distance from point \( X \) to the line of reflection: \( d = y - k \).
2. Since reflection will place the point the same distance on the opposite side of the line, the new y-coordinate \( y' \) will be:
\[
y' = k - d = k - (y - k) = 2k - y
\]
3. The x-coordinate remains unchanged.

Thus, the coordinates of vertex \( X' \) after reflection will be:
\[
X' = (x, 2k - y)
\]

If you provide the coordinates of vertex \( X \) and the line of reflection, I can give you the specific coordinates of \( X' \).