how do you reflect a shape over the x or y axis when its already on the line, like the preimage is already on to of the line, how do you reflect it?

if the original point is on the line of reflection, it just stays there.

but what if none of the points are on it, but the shape it makes is, like a triangle, two points on one side, another on the other.

When reflecting a shape over a line, such as the x or y-axis, and the preimage is already on the line, you can follow these steps to reflect the shape:

1. Identify the line of reflection: Determine whether you are reflecting the shape over the x-axis or the y-axis. This will help you visualize the transformation.

2. Visualize the reflection: Imagine the line of reflection as a mirror. Think about how the shape would appear if it was reflected across the mirror line.

3. Observe the change: Since the preimage is already on the line of reflection, the resulting image will be the same as the original shape. The reflection will essentially reverse the positions of the preimage and the image, but since they overlap, the shape won't change.

4. Verify the result: Double-check that the reflected shape matches the original preimage. If the shape remains in the same position, then the reflection is correct.

In summary, reflecting a shape that is already on the line of reflection results in the shape staying in the same position.

just consider each point. The shape will remain unchanged, just flipped. Just cut out a triangle, and flip it over. Has anything actually changed?