Question

exit ticket ma.7.gr.1.5 scale drawings

objective: students will solve problems involving scale drawings of geometric figures, including computing actual lengths and areas.

1. a map has a scale of 1 inch = 20 miles. if two cities are 4.5 inches apart on the map, what is the actual distance?

1. a blueprint uses a scale of 1:50. if a wall is 10 cm on the blueprint, how many centimeters long is the actual wall?

1. a model car is 6 inches long. the actual car is 180 inches long. what is the scale factor of the model to the actual car?

1. if a 2-inch by 3-inch rectangle is enlarged by a scale factor of 3, what are the new dimensions?

1. a square with a side length of 4 cm is reduced by a scale factor of 0.5. what is the area of the new square?

Explanation:

Set up proportions for map distance

Using the Proportional Relationships knowledge point, we relate map inches to actual miles.

$$ \frac{1\text{ inch}}{20\text{ miles}} = \frac{4.5\text{ inches}}{x\text{ miles}} $$

$$ x = 4.5 \times 20 = 90\text{ miles} $$

Calculate actual blueprint length

Using the Proportional Relationships knowledge point, we apply the ratio of \(1:50\).

$$ \frac{1}{50} = \frac{10\text{ cm}}{y\text{ cm}} $$

$$ y = 10 \times 50 = 500\text{ cm} $$

Determine model car scale factor

We find the ratio of the model length to the actual length.

$$ \text{Scale Factor} = \frac{\text{Model Length}}{\text{Actual Length}} = \frac{6\text{ inches}}{180\text{ inches}} $$

$$ \text{Scale Factor} = \frac{1}{30} $$

Multiply dimensions by scale factor

We multiply each dimension of the original rectangle by the scale factor of 3.

$$ \text{New Width} = 2\text{ inches} \times 3 = 6\text{ inches} $$

$$ \text{New Length} = 3\text{ inches} \times 3 = 9\text{ inches} $$

Calculate scaled square area

We find the new side length, then compute the area.

$$ \text{New Side Length} = 4\text{ cm} \times 0.5 = 2\text{ cm} $$

$$ \text{New Area} = (2\text{ cm})^2 = 4\text{ cm}^2 $$

Answer:

Question 1

90 miles

Question 2

500 cm

Question 3

\(1:30\) (or \(\frac{1}{30}\))

Question 4

6-inch by 9-inch

Question 5

\(4\text{ cm}^2\)