Math Problem Statement
Solution
To address the problem:
Part (a): Steps of Dilations
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Step 1: Dilate the original figure by a scale factor of :
- Each vertex of the triangle is moved to a position that is the distance from the origin (center of dilation).
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Step 2: Dilate the resulting figure by a scale factor of :
- The new figure from Step 1 is again dilated, moving each point to a position times its distance from the origin.
I can create a diagram to visually represent these transformations. Let me know if you'd like that!
Part (b): Equivalent Scale Factor
The combined effect of the two dilations can be found by multiplying the two scale factors together:
Thus, performing Steps 1 and 2 is equivalent to a single dilation centered at the origin with a scale factor of .
Would you like me to visualize or calculate the transformations further? Here are 5 related questions you might want to explore:
- How would you plot the vertices after each transformation step?
- What is the general rule for combining multiple dilations?
- How does the choice of center of dilation affect the transformation?
- Can this method be applied to other geometric figures beyond triangles?
- How would the process change if the dilation centers were not the origin?
Tip: When combining multiple transformations, consider their cumulative effect by multiplying their respective transformation factors.
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Math Problem Analysis
Mathematical Concepts
Geometry
Dilations
Scale Factor
Transformations
Formulas
Combined scale factor = product of individual scale factors
Theorems
Properties of Dilations
Suitable Grade Level
Grades 8-10