Math Problem Statement
Solution
To determine whether the pair of figures (rectangles labeled A and B) represents an original figure and its scaled copy, we need to check if their dimensions follow a consistent scale factor in both directions (width and height).
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Dimensions of Rectangle A (Red):
- Width: 5 units (spanning 5 grid squares horizontally).
- Height: 4 units (spanning 4 grid squares vertically).
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Dimensions of Rectangle B (Purple):
- Width: 3 units (spanning 3 grid squares horizontally).
- Height: 3 units (spanning 3 grid squares vertically).
Scale Factor Check:
For the rectangles to be scaled copies, the ratio of the widths must equal the ratio of the heights. Let’s check:
- Width ratio:
- Height ratio:
Since the width ratio and height ratio are not equal (), these figures are not scaled copies of each other.
The answer to the question is No, they are not a scaled copy.
Would you like further clarification or details?
Relative questions:
- How do you calculate a scale factor between two shapes?
- What makes two figures similar in geometry?
- Can a figure have different scale factors for width and height?
- How would the answer change if both figures were squares?
- What is the relationship between area and scale factor?
Tip: When comparing figures, always check both width and height ratios to confirm if they are scaled versions of each other.
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Math Problem Analysis
Mathematical Concepts
Geometry
Scale Factor
Similarity
Formulas
Width Ratio = Width of A / Width of B
Height Ratio = Height of A / Height of B
Theorems
For figures to be scaled copies, the width ratio and height ratio must be equal.
Suitable Grade Level
Grades 6-8
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