--- title: "Reflections" subtitle: "Angles and shapes · Transformations · Lesson 13" --- # Reflections **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A face in a mirror, a butterfly's wings, a lake showing a mountain. The mirror line sits exactly halfway between each point and its reflection. :::teacher-note **In one sentence:** Students reflect shapes in the x-axis and y-axis and state which coordinate changes sign (AC9M7SP03, node 2). **Students should be able to say:** I can reflect a shape in the x-axis or the y-axis. I can say which coordinate changes sign for each axis. I can check a reflection by its distance from the mirror. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict Picture the point flipping straight down over the x-axis. :::keep-together **Point A is at (2, 1). It is reflected in the x-axis. Where does A′ land?** ☐ (−2, 1) ☐ (1, 2) ☐ (2, −1) ☐ (−2, −1) My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** (2, −1). The point flips over the x-axis, to the same distance below it, so only y changes sign. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Which coordinate changes :::keep-together ### Which axis **B is at (4, 1). It is reflected in the y-axis. Where does B′ land?** ☐ (4, −1) ☐ (−4, 1) ☐ (1, 4) ☐ (−4, −1) ::: :::teacher-note **Answer:** (−4, 1) In the y-axis, x changes sign: (−4, 1). ::: :::keep-together ### Find the mistake **Mia reflects P (4, 3) in the x-axis. Click the line where her reasoning goes wrong.** ``` 1 The point P is (4, 3). Mia reflects it in the x-axis. 2 The x-axis is horizontal, so she changes the x-coordinate. 3 She changes 4 to −4. 4 The image of P is (−4, 3). ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: reflecting in the x-axis moves the point up or down across it, so y changes sign. The image is (4, −3). ::: :::keep-together ### On the mirror **A point is on the mirror line, for example (0, 3) reflected in the y-axis. Where is its image?** ☐ At (3, 0) ☐ In the same place: (0, 3) ☐ At (0, −3) ☐ At (−3, 0) ::: :::teacher-note **Answer:** In the same place: (0, 3) It is zero distance from the mirror, so it does not move: −0 is still 0. ::: :::typical ## Choose the mirror **Reach (4, 1).** **Reach (−2, −4).** **Distance.** **Both mirrors.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Reflections :::keep-together ### y-axis **The point (−4, 6) is reflected in the y-axis. What is the x-coordinate of the image?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 4 x changes sign: −4 becomes 4, so the image is (4, 6). ::: :::keep-together ### x-axis **The point (−4, 6) is reflected in the x-axis. What is the y-coordinate of the image?** Answer: {{field-15}} ::: :::teacher-note **Answer:** -6 y changes sign: 6 becomes −6, so the image is (−4, −6). ::: :::keep-together ### The rule **Which rule describes a reflection in the y-axis?** ☐ (x, y) → (y, x) ☐ (x, y) → (−x, y) ☐ (x, y) → (−x, −y) ☐ (x, y) → (x, −y) ::: :::teacher-note **Answer:** (x, y) → (−x, y) The y-axis is the vertical mirror: x changes sign and y stays. ::: :::keep-together ### Review: translations **Review: the point (2, 3) is translated 4 left and 1 up. What is the x-coordinate of the image?** Answer: {{field-15}} ::: :::teacher-note **Answer:** -2 2 − 4 = −2, so the image is (−2, 4). ::: ## Make: an arrow's mirror image Then write the rule for each mirror in your own words, and say which coordinate stays the same. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **The point (5, −2) is reflected in the x-axis. Where is the image?** {{lines-3}} ::: :::teacher-note **Answer:** (5, 2): y changes sign. :::