--- title: "Translations" subtitle: "Angles and shapes · Transformations · Lesson 12" --- # Translations **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A chess piece slides across the board, a lift goes up, a character steps left on a screen. Each is a translation: every point moves the same way. :::teacher-note **In one sentence:** Students slide a triangle on the coordinate plane and describe the move by the change in each coordinate (AC9M7SP03, node 1). **Students should be able to say:** I can translate a shape and write the new coordinates. I can describe a translation as so many units left or right and up or down. I can say what changes and what stays the same. **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 Add to x for right, take from y for down. :::keep-together **Point A is at (1, 1). The triangle is translated 3 right and 2 down. Where does A land?** ☐ (3, 2) ☐ (4, −1) ☐ (−2, −1) ☐ (4, 3) My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** (4, −1). Right adds 3 to x: 1 + 3 = 4. Down takes 2 from y: 1 − 2 = −1. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Reading the move :::keep-together ### Where does B land? **The triangle has corners A (1, 1), B (3, 1) and C (3, 2). It moves 3 right and 2 down. Where does B land?** ☐ (6, −1) ☐ (6, 3) ☐ (4, −1) ☐ (0, −1) ::: :::teacher-note **Answer:** (6, −1) B′ = (3 + 3, 1 − 2) = (6, −1). ::: :::keep-together ### Find the mistake **Ravi translates A (2, 3) by 4 left and 1 up. Click the line where his reasoning goes wrong.** ``` 1 The point A is (2, 3). The translation is 4 left and 1 up. 2 Left is a move along the x-axis, so I add 4 to x. 3 Up means add 1 to y. 4 The image of A is (6, 4). ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: moving left makes x smaller, so take 4 away: 2 − 4 = −2. The image is (−2, 4). ::: :::keep-together ### What stays the same **What stays the same when a shape is translated?** ☐ Its coordinates ☐ Only its size ☐ Its position ☐ Its size, its shape and the way it faces ::: :::teacher-note **Answer:** Its size, its shape and the way it faces A translation only changes the position. The image is congruent to the object. ::: :::typical ## Choose the move **Aim for A′.** Work out the change in x, then in y. **The fourth quadrant.** **Undo the move.** **Two moves.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Translations :::keep-together ### The x-coordinate **C is at (3, 2). After a translation of 3 right and 2 down, what is the x-coordinate of C′?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 6 3 + 3 = 6. ::: :::keep-together ### The y-coordinate **With the same translation, what is the y-coordinate of C′?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 0 2 − 2 = 0, so C′ = (6, 0). ::: :::keep-together ### Between two points **Which translation takes (2, 5) to (−1, 3)?** ☐ 1 left and 3 down ☐ 3 right and 2 down ☐ 3 left and 2 up ☐ 3 left and 2 down ::: :::teacher-note **Answer:** 3 left and 2 down x goes from 2 to −1 (3 left); y goes from 5 to 3 (2 down). ::: :::keep-together ### Review: quadrants **Review: in which quadrant is the point (−3, 2)?** ☐ Top right ☐ Bottom left ☐ Top left ☐ Bottom right ::: :::teacher-note **Answer:** Top left A negative x is left of the y-axis and a positive y is above the x-axis. ::: ## Make: a move to the origin Then write the translation in words, and as a rule for $(x, y)$. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A (2, 5) is translated 4 left and 3 down. Where is A′?** {{lines-3}} ::: :::teacher-note **Answer:** (−2, 2): x is 2 − 4 = −2 and y is 5 − 3 = 2. :::