Math Problem Statement
Solution
To determine the scale factor of the dilation between the trapezoids and , we need to compare the distances between corresponding points or sides.
Step-by-step process:
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Identify corresponding points:
- The corresponding points of the two trapezoids are , , , and .
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Measure distance between corresponding points:
- Let's find the coordinates of the vertices of trapezoid (larger trapezoid):
- , , , .
- Now the coordinates of the corresponding points of the dilated trapezoid :
- , , , .
- Let's find the coordinates of the vertices of trapezoid (larger trapezoid):
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Calculate distances:
- For simplicity, we will measure the distance between and , as well as between and , to find the scale factor.
- Distance from to the origin: , so its distance from the origin is .
- Distance from to the origin: , so its distance from the origin is .
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Find scale factor:
- The scale factor is the ratio of the distances from the center of dilation (which we assume is the origin):
Thus, the scale factor of the dilation is .
Would you like more details or have any questions?
Here are 5 related questions for further exploration:
- How would the trapezoid's area change if the scale factor was 3 instead of ?
- What is the general formula for the scale factor in dilations centered at the origin?
- How can you determine the center of dilation if it's not given?
- How does the perimeter of a figure change after dilation?
- Can the scale factor be negative, and what would that imply geometrically?
Tip: When finding the scale factor in dilation, always ensure to use the distance between corresponding points, and make sure the center of dilation is clear (often the origin).
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Math Problem Analysis
Mathematical Concepts
Geometry
Dilation
Scale Factor
Formulas
Scale factor = Distance between corresponding points in dilated and original figure / Original distance
Theorems
Dilation Theorem
Suitable Grade Level
Grades 8-10