Question

How can you see that a reflection could work without knowing where the line of reflection is? If you get the answer right I'll paypal, venmo or cash app you $50. So drop your paypal, venmo or cash app along with your answer.

Answer 1

Note how going from R to S to T to U has us going counterclockwise. In contrast, going from R' to S' to T' to U' has us going the opposite direction going clockwise. This change in orientation strongly implies that a reflection has been done. Reflections always flip orientation.

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Here's how we can find the line of reflection.

Draw a line segment from point R to point R'. Mark the midpoint of the segment as point A

Repeat this process to form a segment from S to S'. Mark the midpoint as point B.

The line of reflection will pass through points A and B. This is because the line of reflection is equally distant between the original point (such as point R) and its reflected point (such as R'). This must mean that the line of reflection goes through the midpoint of segment UU' and also segment TT'.

Refer to the diagram below.