Question

Triangle XYZ is reflected over a horizontal line of reflection

Answer 1

When a triangle, such as triangle XYZ, is reflected over a horizontal line of reflection, the following happens:

1. **Positioning of the Reflection Line**: The horizontal line can be seen as a baseline. For example, if the line of reflection is the x-axis, points above this line will move down, and points below will move up.

2. **Vertical Movement**: Each point of the triangle will move perpendicular to the line of reflection to a position that is equidistant on the opposite side of the line. This results in the y-coordinate of each point being negated (if the x-axis is the line of reflection).

3. **Coordinates Transformation**: If the original coordinates of the vertices of triangle XYZ are:
- X(x₁, y₁)
- Y(x₂, y₂)
- Z(x₃, y₃)

For reflection over a horizontal line (e.g., the x-axis), the new coordinates after reflection will be:
- X'(x₁, -y₁)
- Y'(x₂, -y₂)
- Z'(x₃, -y₃)

4. **Shape and Size**: The triangle will maintain its shape and size after reflection, but its orientation will change (the triangle will be flipped).

5. **Visual Representation**: If you visualize it, the triangle will appear as mirrored across the line of reflection.

If you need a specific example or further details, feel free to ask!