Reflections

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by Brian Gervase

| 10 QuestionsNote from the author:

This mini lesson introduces students to the formal definition of a reflection. Students have the opportunity to play with reflections in a guided fashion using Geogebra applets. Let the contest begin!

In this mini-lesson you will get a chance to play with our 3rd type of transformation -- reflections-- and understand the formal definition of a reflection in geometry.

In the sketch below, click the box that says "Reflection Image" and PLAY with the results. Do not click the show measurements yet. Be sure to move ALL points on the screen and try to get a good physical understanding about how the reflection is generated.

1

1

The image of a reflection is congruent to the preimage.

True

False

2

1

Which line above is considered the 'mirror' in this reflection?

AB

BC

CD

AD

EF

3

1

A reflection over a mirror is the same as a 180 degree rotation about a point on the mirror.

True

False

Now click the box in the above sketch that says "Show Measurements". Again play and make some observations about the geometry of the reflection.

4

1

Choose all statements below that are true.

The image and preimage are congruent.

The image COULD be a 180 degree rotation of the preimage.

Line AA' is perpendicular to the mirror.

EF bisects segment DD'.

Segment CC' bisects line EF.

There is a point, Q, on EF such that BQ = B'Q.

5

1

Consider a line on your desk and a point P. Explain how you would find P' , the image of P reflected over the line on your desk. Be specific about what you would have to measure in order to locate P'.

6

1

Use a graph board or Geogebra in another window to visualize and find the indicated point.

Enter the coordinates of P' which is the reflection of P(3,5) over the y-axis.

Enter your answer with no spaces in the form (a,b).

7

1

Use a graph board or Geogebra in another window to visualize and find the indicated point.

Enter the coordinates of P' which is the reflection of P(3,5) over the x-axis.

Enter your answer with no spaces in the form (a,b).

8

1

Use a graph board or Geogebra in another window to visualize and find the indicated point.

Enter the coordinates of P' which is the reflection of P(3,5) over the line y = x.

Enter your answer with no spaces in the form (a,b).

9

1

Use a graph board or Geogebra in another window to visualize and find the indicated point.

Enter the coordinates of P' which is the reflection of P(1,-2) over the line -x + 3y = 3.

Enter your answer with no spaces in the form (a,b).

Hint: Make a GOOD accurate sketch of this and use the coordinate grid to your advantage! This one requires some thought and a close attention to details.

Play the "Flip Flop" game below. You are given the image and preimage of a flip-flop sandle and your goal is to find the mirror that would create that image. Give a try a few times or until you feel like you have mastered it!

The game below gives you a preimage and a mirror. Where does the image land? Use the blue points to construct the "V" shape that is properly reflected. Play with this a few times or until you feel you have mastered it.

10

1

Write about what you have learned about reflections. Be sure to incorporate specific mathematical measurements that are the key to ensuring a proper reflection.

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