It looks like you've uploaded a worksheet titled
"Transformations of Shapes" that asks students to apply geometric transformations (translations, reflections, rotations) to given shapes on the coordinate plane.
Since I can't view images directly, I’ll need you to provide the details of the problem or describe what's in the image. However, based on the typical structure of such worksheets, here’s how these problems are usually solved and explained:
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🔷 Common Types of Transformations:
1.
Translation: Moving a shape by a certain number of units left/right and up/down.
- Example: "Translate 3 units right and 2 units down" → Add 3 to x-coordinates, subtract 2 from y-coordinates.
2.
Reflection: Flipping over a line (e.g., x-axis, y-axis, or y = x).
- Over x-axis: (x, y) → (x, -y)
- Over y-axis: (x, y) → (-x, y)
- Over y = x: (x, y) → (y, x)
3.
Rotation: Turning around a point (usually origin).
- 90° counterclockwise about origin: (x, y) → (-y, x)
- 180°: (x, y) → (-x, -y)
- 270° counterclockwise: (x, y) → (y, -x)
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🔷 How to Solve These Problems:
Let’s assume each question has a triangle or shape plotted on a coordinate grid with labeled points.
#### Example Problem:
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"Translate 3 units right and 2 units down."
Steps:
1. Identify the coordinates of the original vertices.
- Suppose triangle ABC has points A(1, 2), B(3, 4), C(2, 1)
2. Apply the translation:
- Right 3 → add 3 to x
- Down 2 → subtract 2 from y
- New points:
- A'(1+3, 2-2) = (4, 0)
- B'(3+3, 4-2) = (6, 2)
- C'(2+3, 1-2) = (5, -1)
3. Plot the new points and draw the translated triangle.
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🔷 For Reflections:
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"Reflect over the x-axis"
- Change sign of y-coordinate:
- (x, y) → (x, -y)
- So if point is (2, 3), its reflection is (2, -3)
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🔷 For Rotations:
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"Rotate 90° counterclockwise about the origin"
- Use rule: (x, y) → (-y, x)
- Example: (3, 1) → (-1, 3)
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🔷 For Combinations:
Some questions may ask for multiple steps (e.g., translate then reflect). Always do them in order.
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✔ Final Answer Format:
After applying the transformation:
- List the new coordinates.
- Draw the transformed shape on the grid.
- Label the new points (e.g., A', B', C').
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📌 Please Provide:
To help you more accurately, please describe:
1. The specific transformation requested in each question.
2. The coordinates of the original shape (if visible).
3. Or type out the exact wording of one or two problems.
Then I can walk through the solution step-by-step!
Parent Tip: Review the logic above to help your child master the concept of translation math worksheet.
