Unit 7 Lesson 5 Homework (Identifying Transformations) - Josh Agee ... - Free Printable

Let's solve this step-by-step by analyzing each sticky note (A–I) and determining which transformation it represents. Then, we'll match each to the correct category in the table.

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Step 1: Understand the transformations

We need to identify which of the following transformations each sticky note represents:

- Translation Right: x increases (positive direction)
- Translation Left: x decreases (negative direction)
- Translation Up: y increases
- Translation Down: y decreases
- Reflection over x-axis: y-coordinate changes sign → (x, y) → (x, -y)
- Reflection over y-axis: x-coordinate changes sign → (x, y) → (-x, y)
- Rotation 90° clockwise: (x, y) → (y, -x)
- Rotation 180° clockwise: (x, y) → (-x, -y)
- Rotation 270° clockwise: (x, y) → (-y, x)

> Note: Rotation 270° clockwise is equivalent to 90° counterclockwise.

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Now let’s analyze each sticky note:

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Sticky Note A

```
A(-8,7) → A'(-8,-7)
B(-4,7) → B'(-4,-7)
C(-6,2) → C'(-6,-2)
```

- All y-values are negated.
- So: (x, y) → (x, -y)
✔ This is Reflection over x-axis

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Sticky Note B

```
A(-8,7) → A'(8,-7)
B(-4,7) → B'(4,-7)
C(-6,2) → C'(6,-2)
```

- x-coordinates change sign, y-coordinates also change sign?
Wait:
- (-8,7) → (8,-7): x becomes positive, y becomes negative
- So: (x, y) → (-x, -y)? Wait: (-8,7) → (8,-7) → that’s ( -x, -y )? No: -(-8)=8, -(7)=-7 → yes!

So: (x, y) → (-x, -y)

This is a 180° rotation.

✔ Rotation 180° clockwise

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Sticky Note C

```
A(-8,7) → A'(-8,12)
B(-4,7) → B'(-4,12)
C(-6,2) → C'(-6,7)
```

- x stays same, y increases:
- 7 → 12 → +5
- 7 → 12 → +5
- 2 → 7 → +5

All points move up by 5 units

✔ Translation Up

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Sticky Note D

```
A(-8,7) → A'(7,8)
B(-4,7) → B'(7,4)
C(-6,2) → C'(2,6)
```

Let’s check if this fits any rotation.

Try 90° clockwise: (x,y) → (y, -x)

Check A: (-8,7) → (7, 8)? But according to rule: (y, -x) = (7, 8) → YES! Because -(-8) = 8.

Check B: (-4,7) → (7, 4)? Rule: (y, -x) = (7, 4) → YES! Because -(-4) = 4

Check C: (-6,2) → (2, 6)? Rule: (y, -x) = (2, 6) → YES! Because -(-6) = 6

✔ This matches Rotation 90° clockwise

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Sticky Note E

```
A(-8,7) → A'(-13,7)
B(-4,7) → B'(-9,7)
C(-6,2) → C'(-11,2)
```

- y stays same
- x decreases:
- -8 → -13 → -5
- -4 → -9 → -5
- -6 → -11 → -5

So all moved left by 5 units

✔ Translation Left

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Sticky Note F

```
A(-8,7) → A'(8,7)
B(-4,7) → B'(4,7)
C(-6,2) → C'(6,2)
```

- x-coordinates change sign, y stays same
- So: (x,y) → (-x, y)

✔ Reflection over y-axis

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Sticky Note G

```
A(-8,7) → A'(-8,2)
B(-4,7) → B'(-4,2)
C(-6,2) → C'(-6,-3)
```

Wait: y-values decrease, but not consistently?

- A: 7 → 2 → ↓5
- B: 7 → 2 → ↓5
- C: 2 → -3 → ↓5

Yes! All y-values decreased by 5.

So moving down by 5 units

✔ Translation Down

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Sticky Note H

```
A(-8,7) → A'(-7,-8)
B(-4,7) → B'(-7,-4)
C(-6,2) → C'(-2,-6)
```

Let’s test for 270° clockwise → (x,y) → (-y, x)

Check A: (-8,7) → (-7, -8)? According to rule: (-y, x) = (-7, -8) → YES!

Check B: (-4,7) → (-7, -4)? Rule: (-y, x) = (-7, -4) → YES!

Check C: (-6,2) → (-2, -6)? Rule: (-y, x) = (-2, -6) → YES!

✔ Rotation 270° clockwise

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Sticky Note I

```
A(-8,7) → A'(-3,7)
B(-4,7) → B'(1,7)
C(-6,2) → C'(-1,2)
```

- y stays same
- x increases:
- -8 → -3 → +5
- -4 → 1 → +5
- -6 → -1 → +5

So all moved right by 5 units

✔ Translation Right

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Now fill in the table:

| TRANSFORMATION | Letter |
|-------------------------------|--------|
| TRANSLATION RIGHT | I |
| ROTATION 90° CLOCKWISE | D |
| TRANSLATION DOWN | G |
| TRANSLATION LEFT | E |
| ROTATION 180° CLOCKWISE | B |
| TRANSLATION UP | C |
| REFLECTION OVER X-AXIS | A |
| ROTATION 270° CLOCKWISE | H |
| REFLECTION OVER Y-AXIS | F |

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✔ Final Answer Table:

| TRANSFORMATION | Letter |
|-------------------------------|--------|
| TRANSLATION RIGHT | I |
| ROTATION 90° CLOCKWISE | D |
| TRANSLATION DOWN | G |
| TRANSLATION LEFT | E |
| ROTATION 180° CLOCKWISE | B |
| TRANSLATION UP | C |
| REFLECTION OVER X-AXIS | A |
| ROTATION 270° CLOCKWISE | H |
| REFLECTION OVER Y-AXIS | F |

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Summary of Reasoning:

- Reflections: Check sign changes in x or y.
- Translations: Look for consistent changes in x or y.
- Rotations: Use standard rules:
- 90° CW: (x,y) → (y, -x)
- 180°: (x,y) → (-x, -y)
- 270° CW: (x,y) → (-y, x)

Each transformation was verified with all three points to ensure consistency.

✔ All matched correctly!