Problem Analysis:
The worksheet is about
types of dilation in geometry. Dilation is a transformation that changes the size of a figure but not its shape. The scale factor determines whether the dilation is an
enlargement (if the scale factor is greater than 1) or a
reduction (if the scale factor is less than 1).
#### Part A: Identifying Enlargement or Reduction Based on Scale Factor
We need to determine whether each given scale factor represents an enlargement or a reduction.
#### Part B: Identifying the Type of Dilation from Figures
We need to compare Figure A (the dilated image) with Figure B (the original figure) and determine whether the dilation is an enlargement or a reduction.
---
Solution:
####
Part A: State Whether a Dilation with the Given Scale Factor is an Enlargement or a Reduction
1.
Scale factor = 2
- Since \( 2 > 1 \), this is an
enlargement.
-
Answer: Enlargement
2.
Scale factor = \(\frac{1}{8}\)
- Since \( \frac{1}{8} < 1 \), this is a
reduction.
-
Answer: Reduction
3.
Scale factor = \(\frac{5}{4}\)
- Since \( \frac{5}{4} = 1.25 > 1 \), this is an
enlargement.
-
Answer: Enlargement
4.
Scale factor = \(\frac{2}{3}\)
- Since \( \frac{2}{3} \approx 0.67 < 1 \), this is a
reduction.
-
Answer: Reduction
5.
Scale factor = 3
- Since \( 3 > 1 \), this is an
enlargement.
-
Answer: Enlargement
6.
Scale factor = 0.2
- Since \( 0.2 < 1 \), this is a
reduction.
-
Answer: Reduction
---
####
Part B: Identify the Type of Dilation (Reduction or Enlargement)
1.
Figure 1:
- Compare Figure A (larger triangle) with Figure B (smaller triangle).
- Figure A is larger than Figure B, indicating that the dilation is an
enlargement.
-
Answer: Enlargement
2.
Figure 2:
- Compare Figure A (larger rectangle) with Figure B (smaller rectangle).
- Figure A is larger than Figure B, indicating that the dilation is an
enlargement.
-
Answer: Enlargement
3.
Figure 3:
- Compare Figure A (smaller hexagon) with Figure B (larger hexagon).
- Figure A is smaller than Figure B, indicating that the dilation is a
reduction.
-
Answer: Reduction
4.
Figure 4:
- Compare Figure A (smaller triangle) with Figure B (larger triangle).
- Figure A is smaller than Figure B, indicating that the dilation is a
reduction.
-
Answer: Reduction
---
Final Answers:
#### Part A:
1. Enlargement
2. Reduction
3. Enlargement
4. Reduction
5. Enlargement
6. Reduction
#### Part B:
1. Enlargement
2. Enlargement
3. Reduction
4. Reduction
---
Boxed Final Answer:
\[
\boxed{
\begin{array}{ll}
\text{Part A:} & \text{1. Enlargement, 2. Reduction, 3. Enlargement, 4. Reduction, 5. Enlargement, 6. Reduction} \\
\text{Part B:} & \text{1. Enlargement, 2. Enlargement, 3. Reduction, 4. Reduction}
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of dilation worksheet pdf.
