Since I can't view or access images directly, I can’t see the specific figures or coordinates in your uploaded worksheet. However, I can help you
solve the problem and
explain how to find scale factors in dilations based on typical problems like this.
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🔍 What is a Scale Factor?
In geometry, a
scale factor is the ratio of the lengths of corresponding sides of two similar figures. It tells us how much a figure has been enlarged or reduced during a dilation.
- If the scale factor is
greater than 1, the image is
enlarged.
- If the scale factor is
between 0 and 1, the image is
reduced.
- If the scale factor is
negative, the image is reflected across the center of dilation.
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✔ How to Find the Scale Factor
To find the scale factor from
Figure A (original) to
Figure B (dilated image):
1.
Choose a pair of corresponding points on both figures (e.g., vertices).
2.
Find the distance from the center of dilation (often the origin, unless stated otherwise) to each point.
3.
Divide the distance to the image point by the distance to the original point:
$$
\text{Scale Factor} = \frac{\text{Distance from center to image point}}{\text{Distance from center to original point}}
$$
4. Alternatively, pick two corresponding sides and divide their lengths:
$$
\text{Scale Factor} = \frac{\text{Length of side in image}}{\text{Length of corresponding side in original}}
$$
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📌 Example (Typical Problem)
Suppose Figure A has a triangle with a vertex at (2, 0), and the dilated image has a corresponding vertex at (6, 0). The center of dilation is the origin.
- Distance from origin to original: 2 units
- Distance from origin to image: 6 units
- Scale factor = $ \frac{6}{2} = 3 $
✔ So, the scale factor is
3.
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⚠️ Tips for This Worksheet
Look at each pair of figures:
- Identify corresponding vertices.
- Use the grid to measure distances.
- Compare lengths or use coordinates to compute ratios.
For example:
- If one triangle has a base of 4 units and the other has a base of 8 units → scale factor = $ \frac{8}{4} = 2 $
- If a point goes from (3, 0) to (-6, 0), then scale factor = $ \frac{-6}{3} = -2 $ (negative means reflection)
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🧩 Common Mistakes to Avoid
- Don’t assume the center of dilation is always the origin — check if it’s specified.
- Make sure you're comparing
corresponding points.
- Remember: scale factor can be negative (if direction changes).
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📝 Final Answer Format
For each problem, write:
> Scale Factor = [value] (e.g., 2, 0.5, -1.5)
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If you can describe one of the problems (e.g., coordinates of points or shapes), I can walk you through solving it step-by-step!
Parent Tip: Review the logic above to help your child master the concept of geometry dilation worksheet.
