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.

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