To determine the scale factor of a scale drawing, we need to compare the dimensions of the original image to the dimensions of the scale drawing. The scale factor is the ratio of the corresponding dimensions of the scale drawing to the original image. Let's solve each problem step by step.
Problem 1:
Original Image Dimensions:
- Height: 1.25 inches
- Width: 0.75 inches
Scale Drawing Dimensions:
- Height: 1.25 inches (same as original)
- Width: 0.75 inches (same as original)
Scale Factor:
Since both the height and width of the scale drawing are the same as the original image, the scale factor is:
\[
\text{Scale Factor} = \frac{\text{Scale Drawing Dimension}}{\text{Original Image Dimension}} = \frac{1.25}{1.25} = 1
\]
So, the scale factor is:
\[
\boxed{1}
\]
Problem 2:
Original Image Dimensions:
- Length: 2 inches
Scale Drawing Dimensions:
- Length: 3.5 inches
Scale Factor:
\[
\text{Scale Factor} = \frac{\text{Scale Drawing Dimension}}{\text{Original Image Dimension}} = \frac{3.5}{2} = \frac{7}{4}
\]
So, the scale factor is:
\[
\boxed{\frac{7}{4}}
\]
Problem 3:
Original Image Dimensions:
- Length: 1.75 inches
Scale Drawing Dimensions:
- Length: 0.75 inches
Scale Factor:
\[
\text{Scale Factor} = \frac{\text{Scale Drawing Dimension}}{\text{Original Image Dimension}} = \frac{0.75}{1.75} = \frac{3}{7}
\]
So, the scale factor is:
\[
\boxed{\frac{3}{7}}
\]
Problem 4:
Original Image Dimensions:
- Length: 4 cm
Scale Drawing Dimensions:
- Length: 6 cm
Scale Factor:
\[
\text{Scale Factor} = \frac{\text{Scale Drawing Dimension}}{\text{Original Image Dimension}} = \frac{6}{4} = \frac{3}{2}
\]
So, the scale factor is:
\[
\boxed{\frac{3}{2}}
\]
Problem 5:
Original Image Dimensions:
- Length: 12 cm
Scale Drawing Dimensions:
- Length: 6 cm
Scale Factor:
\[
\text{Scale Factor} = \frac{\text{Scale Drawing Dimension}}{\text{Original Image Dimension}} = \frac{6}{12} = \frac{1}{2}
\]
So, the scale factor is:
\[
\boxed{\frac{1}{2}}
\]
Problem 6:
Original Image Dimensions:
- Height: 3 cm
- Width: 5 cm
Scale Drawing Dimensions:
- Height: 3 cm (same as original)
- Width: 5 cm (same as original)
Scale Factor:
Since both the height and width of the scale drawing are the same as the original image, the scale factor is:
\[
\text{Scale Factor} = \frac{\text{Scale Drawing Dimension}}{\text{Original Image Dimension}} = \frac{3}{3} = 1
\]
So, the scale factor is:
\[
\boxed{1}
\]
Final Answers:
\[
\boxed{1, \frac{7}{4}, \frac{3}{7}, \frac{3}{2}, \frac{1}{2}, 1}
\]
Parent Tip: Review the logic above to help your child master the concept of drawing to scale worksheet.
