c. Will this coordinate rule hold true for any figure reflected over the x-axis? Why or why not?
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1 9.1b lass ctivity: Properties of Reflections 1. In the grid below, has been reflected over the y-axis to obtain. 10 a. Describe the movement of a figure that has been reflected. ' b. In the table below, write the coordinates for the vertices of the pre-image and image. Pre-Image Image : : ' : : ' : : c. Write a coordinate rule to describe this reflection. d. Will this coordinate rule hold true for any figure reflected over the y-axis? Why or why not? Directions: Draw and label the image of each figure for the reflection given. Then, answer the questions.. Reflect across the x-axis and label the image. a. In the table below, write the coordinates for the vertices of the preimage and image. 10 Pre-Image : : : : : : Image b. Write a coordinate rule to describe this reflection. c. Will this coordinate rule hold true for any figure reflected over the x-axis? Why or why not? 1 01 University of Utah Middle School Math Project in partnership with the
2 3. Use questions #1 to explore some properties of reflections. a. Go back to problem #1. Draw a segment connecting and, and, and and. Make at least two conjectures about the relationship between the line of reflection and the segments connecting corresponding vertices in the image and pre-image of a reflection. b. Do your conjectures hold true in problem #? c. Go back to problem #1. For a translation we learned that corresponding segments are parallel (have the same slope). Is this property also true for reflections? d. Now, go to problem #. Find the slopes of the following segments: = = = = = = e. ompare the slopes of the corresponding segments of the image and pre-image. What do you notice about the slopes? How does this connect to the coordinate rule (x, y) (x, y)? f. Examine problems #1 and #. What do you notice about the lengths of corresponding segments in the image and pre-image? University of Utah Middle School Math Project in partnership with the
3 . Reflect D across the line y = 1 and label the image. D a. In the table below, write the coordinates for the vertices of the pre-image and image. Pre-Image Image : : : : : : D: D : b. Write a coordinate rule to describe this reflection. 5. Reflect across the line x = 5 and label the image. 15. Reflect over the y-axis and label the image University of Utah Middle School Math Project in partnership with the
4 7. Reflect across the line y = x and label the image. y = x a. Describe the method you used to solve. this problem. b. In the table below, write the coordinates for the vertices of the pre-image and image. Pre-Image Image : : : : : : c. Write a coordinate rule to describe this reflection. e. Find the slopes of the following segments: = = = = = = f. ompare the slopes of the corresponding segments of the image and pre-image. What do you notice? How does this connect to the coordinate rule? d. Will this coordinate rule hold true for any figure reflected over the line y = x? Why or why not? g. onus: What is the coordinate rule for a figure reflected across the line y = x? University of Utah Middle School Math Project in partnership with the
5 . The following table lists the properties of translations discovered in the previous lesson. Put a checkmark in the box if the property is also true for reflections. dd additional statements to the table that are only true for reflections. Properties of Translations Segments connecting the corresponding vertices of the image and pre-image are the same length. Segments connecting the corresponding vertices of the image and pre-image are parallel to each other. lso True for Reflections? *orresponding segments in the image and pre-image are the same length. *orresponding angles in the image and pre-image have the same measure. *Parallel lines in the pre-image remain parallel lines in the image. orresponding segments in the image and pre-image have the same slope University of Utah Middle School Math Project in partnership with the
6 Directions: For #9 11, draw the line of reflection that would reflect one figure onto the other. Then, write the equation for the line of reflection and the coordinate rule that describes the reflection. 9. Draw the line of reflection that would reflect JKLM onto J K L M. J K K' J' M L L' M' 15 a. Write the equation for the line of reflection. b. Write a coordinate rule for the reflection. 10. Draw the line of reflection that would reflect WXY onto W X Y. W' 10 Y X' X Y' W a. Write the equation for the line of reflection. b. Write a coordinate rule for the reflection University of Utah Middle School Math Project in partnership with the
7 11. Draw the line of reflection that would reflect RST onto R S T. S R R' S' 5 10 T T' a. Write the equation for the line of reflection. 01 University of Utah Middle School Math Project in partnership with the
First published in 2013 by the University of Utah in association with the Utah State Office of Education.
First published in 013 by the University of Utah in association with the Utah State Office of Education. opyright 013, Utah State Office of Education. Some rights reserved. This work is published under
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University of Utah Middle School Math Project in partnership with the
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Geometry A Syllabus Credit: one semester (.5) Prerequisites and/or recommended preparation: Completion of Algebra 1 Estimate of hours per week engaged in learning activities: 5 hours of class work per
Investigating the Sine and Cosine Functions Part 1
Investigating the Sine and Cosine Functions Part 1 Name: Period: Date: Set-Up Press. Move down to 5: Cabri Jr and press. Press for the F1 menu and select New. Press for F5 and select Hide/Show > Axes.