Math Problem Statement
Solution
The problem requires plotting the resulting image of the figure after applying a dilation by a factor of centered at the origin. Let's work through the solution step by step.
Steps to Solve:
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Understand Dilation:
- A dilation transformation scales the coordinates of each vertex of the figure by the dilation factor , relative to the center of dilation (in this case, the origin).
- Formula: .
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Apply Dilation Factor :
- Each vertex of the original figure will have its and -coordinates multiplied by .
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Original Coordinates of Vertices: From the image, approximate coordinates of the vertices are:
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Calculate New Coordinates: Using :
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Plot the New Image:
- Draw the quadrilateral connecting the points , , , and .
Would you like me to sketch the resulting transformation for you? Let me know if you want additional explanations or further assistance!
Related Questions:
- What happens to the area of a figure when it is dilated by a factor of ?
- How would the coordinates change if the dilation factor were instead of ?
- What are some real-world applications of dilation transformations?
- How does the center of dilation impact the transformed figure?
- Can a dilation result in a figure with overlapping or negative coordinates? Why or why not?
Tip:
Always double-check your vertex coordinates before applying transformations to ensure accuracy.
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Math Problem Analysis
Mathematical Concepts
Dilation
Transformations
Coordinate Geometry
Formulas
(x, y) → (kx, ky)
Theorems
Basic properties of dilation
Suitable Grade Level
Grades 8-10
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