Math Problem Statement

or The parallelogram D'E'F'G' is a dilation of the parallelogram DEFG. What is the scale factor of the dilation?

Solution

To determine the scale factor of the dilation between parallelogram DEFGD'E'F'G' and DEFGDEFG, we need to compare corresponding side lengths of the two parallelograms.

From the given image:

  • Side DEDE of the original parallelogram corresponds to side DED'E' of the dilated parallelogram.
  • The length of DEDE is 2 units, and the length of DED'E' is 6 units.

Formula for scale factor:

Scale Factor=Length of side in the dilated figureLength of side in the original figure\text{Scale Factor} = \frac{\text{Length of side in the dilated figure}}{\text{Length of side in the original figure}}

Substitute the values: Scale Factor=62=3\text{Scale Factor} = \frac{6}{2} = 3

Final Answer:

The scale factor of the dilation is 3.

Would you like a detailed explanation on dilation or how to calculate scale factors?


Related Questions:

  1. How do you find the scale factor if the areas of the figures are given?
  2. What happens to the angles of a figure during a dilation?
  3. How do you calculate a scale factor if the coordinates of vertices are provided?
  4. How does a dilation affect the perimeter of a shape?
  5. Can a dilation have a scale factor less than 1? What does it mean?

Tip: Always ensure that you compare corresponding sides or dimensions to calculate the scale factor correctly.

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Math Problem Analysis

Mathematical Concepts

Geometry
Dilations
Scale Factor

Formulas

Scale Factor = Length of side in the dilated figure / Length of side in the original figure

Theorems

Properties of Dilations

Suitable Grade Level

Grades 6-8