1. What is a Scale Drawing?

A scale drawing is a proportional, two-dimensional representation of an object or area that is larger or smaller than its actual size. Scale drawings preserve the shape of the original figure while altering its size.

Scale: The defined ratio comparing the dimensions in the drawing to the corresponding actual dimensions.
$$\text{Scale} = \frac{\text{Drawing Distance}}{\text{Actual Distance}}$$

• Example: $\text{1 inch} = \text{5 feet}$ means every $1\text{ inch}$ on the paper represents $5\text{ feet}$ in real life.

2. Understanding Scale Factor

The Scale Factor is a unitless ratio comparing the size of the drawing to the size of the real object. To calculate the scale factor, both measurements must be converted to the same unit:

1. Write the scale as a ratio: $\frac{\text{Drawing Size}}{\text{Actual Size}}$
2. Convert both measurements to matching units (e.g., inches to inches, feet to feet).
3. Simplify the ratio.

Formula:

$$\text{Scale Factor} = \frac{\text{Scaled Measurement}}{\text{Actual Measurement (in same units)}}$$

3. How to Calculate Actual Dimensions

To find the actual distance using a scale drawing:

1. Set up a proportion:
   $$\frac{\text{Scale Drawing Units}}{\text{Scale Actual Units}} = \frac{\text{Given Drawing Distance}}{\text{Unknown Actual Distance ($x$)}}$$
2. Cross-multiply and solve for $x$.

• Example Walkthrough:
• • Scale: $1\text{ cm} = 4\text{ meters}$
  • Drawing Length: $3.5\text{ cm}$
  • Calculation:
    $$\frac{1\text{ cm}}{4\text{ m}} = \frac{3.5\text{ cm}}{x\text{ m}}$$
    $$1 \cdot x = 4 \cdot 3.5 \implies x = 14\text{ meters}$$

A scale drawing shows a real object at a proportional size. The scale (e.g., 1 cm : 2 m) tells you how a length on the drawing relates to the real length. Work through each item and use the hints if you get stuck — nothing here is graded.