Graphing & Describing “Translations” Chapter 6 Day 3 __________________ Graphing & Describing “Translations”

We learned that there are 4 types of Transformations Previously… We learned that there are 4 types of Transformations

Today… Our lesson is going to be ALL about translations.

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. Make sure students recognize a translation when they see one. Notice how the pre-image and image are both pointing in the same direction. This is how the student can tell a translation from a reflection. On a reflection, the pre-image and image will be pointing in opposite directions.

Let’s take a second and see if we understand how to slide left, right, up and down. Click for web page

Let’s Get Started… Section 1: Performing a Translation (Slide) Section 2: Describing a Translation

How do I perform a translation like the one seen below? Let’s see…

Steps Translate ∆𝑨𝑩𝑪 : 7 units right and 4 units up 1) You can start with any vertex, but let’s start with A. Move right 7 units and up 4 units. Draw a dot and label it A′. 2) Then repeat Step 1 for the other vertices. 3) Connect the dots. Demonstrate on the board and explain how to translate. List the coordinates of preimage and image. Pre-Image Image 𝑨(−𝟔, −𝟑) 𝑨′(𝟏, 𝟏) 𝑩(−𝟐, −𝟑) 𝑩′(𝟓, 𝟏) 𝑪(−𝟐, 𝟑) 𝑪′(𝟓, 𝟕) NAME THE COORDINATES Pre-image Image

What Happened to the Coordinates? Pre-Image Image 𝑨(−𝟔, −𝟑) 𝑨′(𝟏, 𝟏) B(−𝟐, −𝟑) 𝑩′(𝟓, 𝟏) 𝑪(−𝟐, 𝟑) 𝑪′(𝟓, 𝟕) Moving right 7 units added 7 to the x-coordinate. Moving up 4 units added 4 to the y-coordinate. Translate ∆𝑨𝑩𝑪: right 7 and up 4 Discuss what happened to the coordinates after the figure was translated as indicated on this slide. Click mouse and then discuss that when a translation is performed, the movement does not effect the figures size or shape. It is preserved. The pre-image and image are (and will always be) congruent when a translation is preformed. 8.G.1, 8.G.2, and 8.G.3 are all based on the students knowing this fact. What Happened to the Figure? Are the line segments in the pre-image and image the same length? In other words… was the size of the figure preserved? Are the pre-image and image congruent then?

GUIDED PRACTICE A B C D Translate: left 2 units and down 5 units COORDINATES Pre-image Image A B C D Work problem on the board. Have students follow along in their student notes. Pre-Image Image A(4,4) A’(2,-1) B(8,4) B’(6,-1) C(6,2) C’(4,-3) D(2,2) D’(0,-3) GUIDED PRACTICE

What Happened to the Coordinates? Pre-Image Image 𝑨(𝟒, 𝟒) 𝑨′(𝟐, −𝟏) B(𝟖, 𝟒) 𝑩′(𝟔,−𝟏) 𝑪(𝟔, 𝟐) 𝑪′(𝟒,−𝟑) 𝑫(𝟐, 𝟐) 𝑫′(𝟎,− 𝟑) Moving left 2 units subtracted 2 from the x-coordinate. Moving down 5 units subtracted 5 from the y-coordinate. Translate: left 2 and down 5 Discuss what happened to the coordinates after the figure was translated as indicated on this slide. Click mouse and then discuss again that when a translation is performed, the movement does not effect the figures size or shape. It is preserved. The pre-image and image are congruent. Are the line segments in the pre-image and image the same length? In other words… was the size of the figure preserved? Are the pre-image and image congruent then? What Happened to the Figure?

YOU TRY #1 W X Y Z Translate: 4 units right and 2 units down COORDINATES Pre-image Image W X Y Z Pre-Image Image W(-9,6) W’(-5,4) X(-4,6) X’(0,4) Y(-9,3) Y’(-5,1) Z(-4,3) Z’(0,1) YOU TRY #1

YOU TRY #2 A B D C Translate: 10 units left COORDINATES Pre-image Image A B C D Pre-Image Image A(4, -3) A’(-6, -3) B(8, -4) B’(-2, -4) C(5, -7) C’(-5,-7) D(3, -5) D’(-7, -5) YOU TRY #2

Moving On… Section 1: Performing a Translation (Slide) Section 2: Describing a Translation

In Section 1 of this PowerPoint… You were given a description of a translation and then asked to perform it on a coordinate plane. In this Section… You will be given a translation that has already been performed and then will be asked to describe what happened.

Writing a RULE using WORDS To describe a translation… Pick any vertex on the pre-image and write how many units the corresponding vertex on the image was moved left or right. Then do the same and write how many units it was move up or down. Tell students that it is common practice to list the left/right movement first when describing a translation. Strongly point out that they have to start with the pre-image and NOT the image! I can see some of the students making this mistake. Rule: right 9 units and up 4 units

You Try #1 left 7 units and up 4 units Again… remind students that they have to start with the pre-image.

You Try #2 right 4 units and down 6 units Again… remind students that they have to start with the pre-image.

Sometimes, a problem might not use words when describing a translation Sometimes, a problem might not use words when describing a translation. It might use symbols. You might see something like this: (𝐱, 𝐲)→ (𝐱+𝟒, 𝐲−𝟏) It means to take the pre-image coordinates and move: right 4 and down 1 This means that you take the original coordinates from the preimage (x, y) and translate it --> as indicated. The x-coordinate controls the left/right movement. Adding means move right. Subtracting means move left. The y-coordinate controls the up/down movement. Adding means move up. Subtracting means to move down.

Guided Practice What rule describes the translation shown? A (x,y) → (x - 4, y - 6) D' F' E B (x,y) → (x - 6, y - 4) D C (x,y) → (x + 6, y + 4) F G' D (x,y) → (x + 4, y + 6) G Answer: C

You Try What rule describes the translation shown? A (x,y) → (x + 8, y - 5) B E' (x,y) → (x - 5, y - 1) D' C (x,y) → (x + 5, y - 8) F' D (x,y) → (x - 8, y + 5) E D G' F Answer: D G

Questions 1) What is a translation? 2) What are congruent figures? 3) Will a translation always result in a congruent figure? 4) Does a slide to the right add or subtract from the x-coordinate? What about a slide to the left? 5) What does a slide up or down do to the y-coordinate? 1) 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. 2) Figures that have the exact same shape and size. If two figures are congruent, then a transformation (or series of transformations) will MAP one figure onto the other. 3) Yes 4) Sliding right adds to the x-coordinate. Sliding left subtracts from the x-coordinate. 5) Sliding up adds to the y-coordinate. Sliding down subtracts from the y-coordinate.

END OF POWERPOINT