Math Problem Statement
Solution
Let's analyze the transformations that map pentagon PQRST onto P'Q'R'S'T'.
Step 1: Identify the Relationship Between PQRST and P'Q'R'S'T'
- The original pentagon PQRST is in the first quadrant.
- The transformed pentagon P'Q'R'S'T' is in the second quadrant, which suggests a reflection or rotation.
Step 2: Test Possible Transformations
Option 1: Reflection Across the y-axis Followed by a Translation Right 4 Units and Up 3 Units
- A reflection over the y-axis would place the shape in the second quadrant, which matches the new location.
- However, reflecting the shape over the y-axis flips the orientation, but does not align it properly.
- A translation of right 4, up 3 does not fully match the new pentagon.
✅ This option seems incorrect.
Option 2: Translation Left 4 Units and Down 7 Units, then Rotation 180°
- Moving left 4 units and down 7 units shifts the shape, but the orientation remains the same.
- A 180° rotation would correctly align it by flipping it around the origin.
✅ This option appears to be correct!
Option 3: Rotation 90° Clockwise, then Translation Left 4 Units and Up 12 Units
- A 90° clockwise rotation would place the shape in a different orientation.
- Translation left 4, up 12 would not correctly align the figure.
✅ This option is incorrect.
Conclusion:
The correct answer is "A translation left 4 units and down 7 units followed by a rotation 180° around the origin."
Would you like a step-by-step coordinate transformation breakdown?
5 Related Questions:
- What happens to coordinates when reflected across the y-axis?
- How do you determine the correct transformation sequence for shapes?
- What is the effect of a 180° rotation on a shape?
- How can you verify transformations using coordinate points?
- What transformations preserve shape size and orientation?
Tip:
When analyzing transformations, always check orientation, position, and size before selecting an answer!
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Math Problem Analysis
Mathematical Concepts
Geometric Transformations
Coordinate Geometry
Formulas
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Theorems
Reflection across the y-axis
Rotation 180°
Translation of points
Suitable Grade Level
Grade 8-9
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