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Reflections over Parallel Lines: Distances

Author:Bob Allen
We've explored reflections, rotations, and translations. Now we're going to go a bit more basic and work only with reflections. You will be exploring what happens to a figure when reflected over two parallel lines. REMEMBER: Mistakes are a good thing. No one, and I mean no one, gets every construction right on the first try. This isn't brain surgery. Nothing will crash if you make a mistake. And starting over is sometimes the best way to go. So there's the do over symbol in the upper right hand corner.

Instructions for the first set of reflections.

1. Measure the distance DE. 2. Measure the distance from point D to any part of line f that's not a point. You might have to use the Move tool to move the two measurements off of one another. 3. Using the Reflect about Line tool, reflect ABC over line f. 4. Using the Reflect about Line tool, reflect A'B'C' over line g.

Distance from a point to a line

1. Why are the two distances, DE and Df, the same? (And if they're not the same, you have done something incorrect. Go back and try again. Remember, nothing has exploded. Not even your grade.) Hint: What distance are we measuring from a point to a line?

Collecting Data

2. Measure the distance from A to A''. Record the distance between the lines (either DE or Df) and AA'' in the box below and call it 'Trial 1." Then move any or all of the following objects: the pink dots on line f, point D, or ABC. Record the distance between the lines and AA'' and label it Trial 2 in the box below. Repeat the previous step three more times, labelling new steps as Trials 3 through 5 respectively. Your data should look something like this: Trial 1 ### ### Trial 2 ### ### and so on.

Conjecturing

Compare the two distances recorded in the five trials above. State a conjecture about the two distances. Here's a start... If a figure is reflected over two parallel lines, then...

Press the Turn In button ONCE and then wait patiently for a few moments. If nothing seems to happen, or if you do not have a Turn In button, call for me.

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