Chapter 6 Day 4 Graphing & Describing Reflections We have learned that there are 4 types of transformations: 1) 2) 3) 4) Translations

Reflections Rotations Dilations The first 3 transformations preserve the size and shape of the figure. In other words If your pre-image (the before) is a trapezoid, your image (the after) is a congruent trapezoid.

If your pre-image contains parallel lines, contains congruent parallel lines . If your pre-image is an angle, angle with the same measure. your image your image is an Yesterday our lesson was ALL about translations.

Today our lesson will focus on reflections. Lets Get Started Section 1: Comparing a translation to a reflection. Section 2: Performing a reflection over the x- or y-axis. Section 3: Performing a reflection over a line.

Section 4: Describing a reflection. Turn and Discuss Which of the below is the translation and which is the reflection. Be ready to explain how you know to the class. #1 #2

Turn and Discuss Which of the below is the translation and which is the reflection. Be ready to explain how you know to the class. #1 #2 If You Remember A translation is a slide that moves a figure to a different position (left, right, up or down) without changing its size or

shape and without flipping or turning it. You can use a slide arrow to show the direction and distance of the movement. A reflection (flip) creates a mirror image of a figure. Moving On Section 1: Comparing a translation to a reflection. Section 2: Performing a reflection over the x- or y-axis.

Section 3: Performing a reflection over a line. Section 4: Describing a reflection. A Reflection is a Flip over a Line A reflection is a flip because the figure is flipped over a line. Each point in the image is the same distance from the line as the original point. t

A' A B C C' B' A and A' are both 6 units from line t.

B and B' are both 6 units from line t. C and C' are both 3 units from line t. Each vertex in ABC is the same distance from line t as the vertices in A'B'C'. Check to see if the pre-image and image are congruent. STEPS and EXAMPLE Reflect the figure across the y-axis. Step 1: Start with any vertex and count the number

of units to the specified axis (or line). Step 2: Measure the same distance on the other side of the axis (or line) and place a dot. Label using prime notation. Step 3: Repeat for the other vertices. Check to see if the pre-image and image are congruent. Reflection Across the Y-AXIS

Lets name the coordinates of each figure. reflection across y-axis Pre-image Image A( ,

) A' ( , ) B( , )

B' ( , ) C( , )

C' ( , ) D( , ) D' (

, ) ----- When you reflect across the y-axis ----- Compare the coordinates of the pre-image to thestay image. The y-coordinate will always

the same. The x-coordinate will always flip signs. What do you notice? Lets take a look at the same pre-image and see what it looks like after being reflected across the x-axis Reflection Across the X-AXIS Here is the same pre-image but this time it is reflected across the x-axis. Pre-image Image

reflection across x-axis ------ When you reflect the x-axis Compare the across coordinates of-----the pre-image to the image.

The x-coordinate will always stay the same. The y-coordinate will always flip signs. What do you notice? Reflect across the y-axis. Name the coordinates of your reflection: You Try #1

Reflect figure QRST across the x-axis Name the coordinates of your reflection: You Try #2 Turn and Discuss Which could be a point reflected across the x-axis? Which could be a point reflected across the y-axis? Be prepared to explain how you know to the class.

A. B. C. Moving On Section 1: Comparing a translation to a reflection. Section 2: Performing a reflection over the x or y-axis. Section 3: Performing a reflection over a line.

Section 4: Describing a reflection. Reflections Across a Vertical or Horizontal Line You may be asked to reflect a figure across a line that is not the x-axis or the y-axis. Lets see how to do that Example over a Vertical Line line of reflection

First, draw the line of reflection. Then follow the normal steps for reflecting over a line. Example over a Horizontal Line First, draw the line of reflection. line of reflection

Then follow the normal steps for reflecting over a line. Reflect across the line Name the coordinates of your reflection: You Try #3

Reflect figure ABCD across the line Name the coordinates of your reflection: You Try #4 Moving On Section 1: Comparing a translation to a reflection. Section 2: Performing a reflection over the x or y-axis. Section 3:

Performing a reflection over a line. Section 4: Describing a reflection. Describing a Reflection In this Section, you will be given a reflection that has already been performed, and you will describe what occurred. Example:

Description reflection across You Try Describe the below reflections. 5) 6) You Try 7) Which of the following represents a single Figure 1? Figure 1

A C B D reflection of You Try 8) Describe the reflection below.

A) across the y-axis B) across the x-axis C) across the line y=-3 D) across the line x=4 You Try Describe the below reflection of point (3,-7). 9) A. reflection across the x-axis B. reflection across the y-axis Questions

1) What is the difference between a translation and a reflection? 2) How do you perform a reflection? 3) Will a reflection ALWAYS result in a congruent figure? 4) How would you complete this if it was a reflection over the x-axis? (9, 3) ( , ) 5) How would you complete this if it was a reflection over the (9, 3) ( , ) 6) How do describe a reflection?

y-axis? END OF POWERPOINT