Interactive quiz: Enlargements, reductions, and scale factors Grade 7

📚 Quick Study Guide

• 📐 Enlargement: An enlargement increases the size of an object. The scale factor is greater than 1.
• 📉 Reduction: A reduction decreases the size of an object. The scale factor is between 0 and 1.
• 🔢 Scale Factor: The ratio of the length of the new image to the length of the original image. It's calculated as: $\text{Scale Factor} = \frac{\text{New Length}}{\text{Original Length}}$.
• 📏 Finding New Length: To find the new length after enlargement or reduction, multiply the original length by the scale factor: $\text{New Length} = \text{Original Length} \times \text{Scale Factor}$.
• 💡 Important Note: If the scale factor is 1, the size of the object remains the same.

✍️ Practice Quiz

1. Question 1: A square with a side length of 5 cm is enlarged by a scale factor of 3. What is the side length of the new square?
   1. 2 cm
   2. 8 cm
   3. 15 cm
   4. 25 cm
2. Question 2: A rectangle with a length of 8 cm and a width of 4 cm is reduced by a scale factor of 0.5. What is the new length of the rectangle?
   1. 2 cm
   2. 4 cm
   3. 6 cm
   4. 16 cm
3. Question 3: A triangle has a base of 10 cm. If the base is enlarged to 25 cm, what is the scale factor?
   1. 0.4
   2. 1.5
   3. 2.5
   4. 3.5
4. Question 4: A circle with a radius of 6 cm is reduced by a scale factor of $\frac{1}{3}$. What is the radius of the new circle?
   1. 1 cm
   2. 2 cm
   3. 3 cm
   4. 18 cm
5. Question 5: A line segment is 12 cm long. After an enlargement, it becomes 36 cm long. What is the scale factor?
   1. 2
   2. 3
   3. 4
   4. 5
6. Question 6: A photo is 15 cm wide and 10 cm tall. It is reduced by a scale factor of 0.8. What are the new dimensions?
   1. 12 cm wide and 8 cm tall
   2. 10 cm wide and 7 cm tall
   3. 18.75 cm wide and 12.5 cm tall
   4. 15.8 cm wide and 10.8 cm tall
7. Question 7: A shape has an area of 20 $cm^2$. It's enlarged by a scale factor of 2. What is the new area?
   1. 10 $cm^2$
   2. 40 $cm^2$
   3. 60 $cm^2$
   4. 80 $cm^2$