Year 7 Transformations Dr J Frost jfrosttiffin kingston

Year 7 Transformations Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths. com Objectives: Be able to both describe and carry out: (a) translations, (b) reflections, (c) rotations. Appreciate that some combinations of transformations can be expressed as a single transformation. Last modified: 21 st June 2016

8 Overview of 4 types of transformation 6 4 A ‘transformation’ is applying some spatial modification to a shape. There are 4 main types of transformation… 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 Click to ROTATE Click to REFLECT Click to -6 TRANSLATE Click to ENLARGE (Note: Tiffin Boys don’t cover until Year 9)

In Your Book For each of translation, reflection and rotation, we will learn how to: (a) DESCRIBE a transformation and (b) DO a transformation yourself. Take one full page in your book in ‘landscape’ format, and draw the following table: Translation Describing Doing Reflection Rotation

Translation 8 6 4 2 B A -10 -8 -6 -4 -2 2 4 6 8 10 Describing What type ? -2 -4 What else can we say ? -6 The first mark of any ‘describe’ question comes from identifying which type of transformation it is.

Update Your Table Translation Describing (Focus on one point) Doing As above. Reflection Rotation

More Examples 8 Describe the transformation from A to B in each case. A Describe ? A 2 B 4 B 6 -10 -8 -6 -4 -2 2 4 6 8 10 -2 A -4 A B Describe ? -6 B Describe ?

Check Your Understanding 8 (On your printed sheet) 6 B 4 D C A R 2 Q -10 -8 -6 -4 -2 2 4 6 8 10 E F -2 -4 Reveal -6 ? ? ?

Exercise 1 8 (On your printed sheet) 6 C . D . 4 B . 2 A . E . -10 -8 -6 -4 -2 2 4 6 8 10 -2 G . F . -4 ? ? ? -6 ? ? ?

Exercise 1 – Question 2 8 (On your printed sheet) 6 4 A C X 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 Draw > -6 B

Exercise 1 3 (On your printed sheet) ? 4 ? ? N ?

Reflection 8 6 ? 4 2 ? -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6

Reflection 8 6 ? 4 2 ? -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6

Mini-Exercise (on sheet) By considering points on each line and observing any pattern, determine the equation the represents the line. 8 6 4 A 2 ? -10 -8 -6 -4 -2 2 4 6 8 10 -2 B ? -4 -6 N C ? ?

Describing reflections 8 6 Click to IDENTIFY LINE OF REFLECTION 4 A 2 B -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 ? -6

Further Example 8 6 Click to IDENTIFY LINE OF REFLECTION 4 A 2 -10 -8 -6 -4 -2 2 4 6 8 10 ? -4 -6 B -2

Test Your Understanding 8 6 4 D A B 2 -10 -8 -6 -4 -2 2 4 6 8 10 C -2 -4 -6 ? ? ?

DOING a reflection 8 6 4 A 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 STEP 1: Draw the reflection line using the given equation. STEP 2: For each point on your shape, move directly towards the reflection line. Then go the same number of squares beyond. -4 -6

Further Example 8 6 4 A 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6

Test Your Understanding 8 6 4 A 2 -10 -8 -6 -4 -2 2 4 6 8 10 CC -2 BB -4 -6 Reveal >

Update Your Table Translation Describing Reflection “A reflection in the line …. ” (Focus on one point) Doing As above. Do point by point. Count squares. Rotation

Exercise 2 – Question 1 A Click to show solutions B C Reflect each shape in the nearest line of reflection.

Exercise 2 – Question 2 8 E 6 4 A A 2 B C -10 -8 -6 -4 -2 2 4 6 8 10 C -2 B -4 D -6 Click to show solutions

Exercise 2 – Question 3 8 6 C 4 A . A 2 B D -10 -8 -6 -4 -2 2 4 6 8 10 C -2 -4 ? ? ? -6 B

Exercise 2 – Question 4 8 6 4 Click to show solutions A 2 Bob -10 -8 -6 -4 -2 2 4 6 8 10 -2 C Steve -4 -6 B

Exercise 2 – Question 5 A Click to show solutions B C

Exercise 2 – Question 6 8 6 A C 4 A 2 B -10 -8 -6 -4 -2 2 4 6 8 10 C D B -2 -4 -6 ? ? ?

Exercise 2 ? ? ? ?

Doing Rotation 8 6 4 A Step 1: Draw in your centre of rotation! A 2 A Step 2: For each point on your shape, count the squares left/right and up/down to the centre of rotation, then go that number of squares again. -10 -8 -6 -4 -2 2 4 6 8 10 C -2 -4 -6 B Bro Tip: Students often try to ‘second guess’ the remaining points, and frequently get it wrong when they do so.

8 6 Step 1: Draw in your centre of rotation! A Step 2: This time, for 4 each point, the counts A SWAP, i. e. left/right A becomes up/down 2 2 and vice versa. 1 Use common sense to 2 1 get the correct direction. -10 -8 -6 -4 -2 2 4 6 8 10 C -2 -4 -6 B

Test Your Understanding 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6

Test Your Understanding 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 Rotate the object 180° That rotation was about the point (1, 1). misshapen and unsightly. . . -6 like your face.

8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 Not bad, but my dog has Rotate the object 90° more rotation skill than -6 anticlockwise about the you do. point (2, 2).

8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 I’ll tell you what. . . That was one phenomenal Rotate the object 90° -6 rotation performance. clockwise about the origin.

Rotation - Describing 8 6 Reminder: The original shape is known as the: OBJECT ? 4 A 2 -10 -8 -6 -4 -2 2 4 6 8 10 C Click to ROTATE BReminder: -2 The shape after being transformed is known as the: IMAGE ? -4 -6 ? ? ?

Identifying the centre of rotation 8 ? 6 4 Object 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 Image -4 ? ? ? -6

8 Identifying the centre of rotation 6 Image We can see this point works because the counts of 3 and 1 squares ‘swap’. And it looks like a right angle! 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 Object -4 -6

8 Another Example 6 Image 4 Object 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6

Update Your Table Translation Describing Reflection “A reflection in the line …. ” Rotation (Focus on one point) Doing As above. Do point by point. Count squares.

Test Your Understanding 8 6 ? 4 B C 2 ? -10 -8 -6 -4 -2 2 4 6 8 10 A -2 -4 -6 D

Exercise 3 – Question 1 8 6 4 A 2 -10 -8 -6 -4 -2 2 4 6 8 10 B -2 Click to show solutions C -4 -6

Exercise 3 – Question 2 8 6 4 ? A 2 ? B -10 -8 -6 -4 -2 2 4 6 8 10 -2 B -4 -6 C

Exercise 3 – Question 3 8 6 4 A 2 B C -10 -8 -6 -4 -2 2 4 6 8 10 D -2 Draw > -4 Draw > -6 Draw >

Exercise 3 – Question 4 8 6 ? 4 ? A 2 ? B -10 -8 -6 -4 -2 2 4 6 8 10 -2 B C -4 -6 D

Exercise 3 – Question 5 8 6 ? ? D 4 2 C B -10 -8 -6 -4 -2 2 4 6 8 10 A -2 -4 -6 B

Exercise 3 ? ? ? ?

Combined Transformations Investigation Working in groups, determine a single transformation that has the same effect as the two transformations listed. (You may wish to use an example shape to help you) Write the question and answer in your books. ? Example Obj Why would it have been a bad idea to use a square? We wouldn’t be able to tell whether the single transformation was a rotation or a reflection. Use nonisosceles right-angled triangles. ? Img (Questions on next slide)

Combined Transformations Investigation Working in groups, determine a single transformation that has the same effect as the two transformations listed. (You may wish to use an example shape to help you) Write the question and answer in your books. 1 2 3 4 5 N ? ? ?

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