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Scale Drawings

Master scale drawings with interactive lessons and practice problems! Designed for students like you!

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Scale Drawings

Study Guide

Key Definition

A scale drawing is a representation of an object where all dimensions are proportionally reduced or enlarged by a certain factor, known as the <a href="scale-factor">$\text{scale factor}$</a>.

Important Notes

A scale factor is a ratio that compares the scaled measurement to the actual measurement.
To find a real distance from a scale drawing, multiply the drawing distance by the scale factor.
In scale drawings, all corresponding lengths are proportional.
Scale drawings are used in maps, blueprints, and models.
Always check units when working with scale factors.

Mathematical Notation

$1 : n$ indicates 1 unit on the drawing equals n units in reality

$n : 1$ indicates n units on the drawing equal 1 unit in reality

$\frac{\text{drawing size}}{\text{actual size}}$ expresses the scale factor

$\times$ represents multiplication and $\div$ represents division in scale calculations

Remember to use proper notation when solving problems

Why It Works

Scale drawings work because they maintain the proportions between the original object and the drawing. Using a consistent scale factor ensures that all parts of the object are represented accurately in the drawing.

Remember

A scale factor of $1 : 100$ means that 1 unit on the drawing represents 100 units in reality.

Quick Reference

Scale Factor:$\text{scale factor} = \frac{\text{drawing size}}{\text{actual size}}$

Understanding Scale Drawings

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A scale drawing is a representation where each measurement is proportional to the actual object by a constant called the scale factor. If the scale is $1 : n$, then 1 unit on the drawing equals n units in reality. For example, on a map with scale $1 : 1000$, 1 cm on the map represents 1000 cm, or 10 m, in real life.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

In a scale drawing with a scale factor of $1 : 100$, a distance of $4 \text{ cm}$ on the drawing represents how many meters in reality?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You want to create a model of a park using a scale factor of $1 : 500$. If the actual distance between the entrance and the lake is $1000 \text{ m}$, what is the distance on your model?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

A model of a stadium uses a scale factor of $1 : 2000$. If the model length of the stadium is $3 \text{ cm}$, find the actual length.

Challenge Quiz

Single Choice Quiz

Advanced

An enlarged scale drawing of an electronic chip has dimensions of $8 \text{ cm} \times 4 \text{ cm}$. The actual chip is $2 \text{ mm} \times 1 \text{ mm}$. What is the scale factor?

Recap

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