# Lesson 1

Scale Drawings

- Let’s make a scale drawing.

### 1.1: Is That the Same Hippo?

Diego took a picture of a hippo and then edited it. Which is the distorted image? How can you tell?

Is there anything about the pictures you could measure to test whether there’s been a distortion?

### 1.2: Sketching Stretching

A **dilation** with center \(O\) and positive **scale factor** \(r\) takes a point \(P\) along the ray \(OP\) to another point whose distance is \(r\) times farther away from \(O\) than \(P\) is. If \(r\) is less than 1 then the new point is really closer to \(O\), not farther away.

- Dilate \(H\) using \(C\) as the center and a scale factor of 3. \(H\) is 40 mm from \(C\).

- Dilate \(K\) using \(O\) as the center and a scale factor of \(\frac{3}{4}\). \(K\) is 40 mm from \(O\).

### 1.3: Mini Me

- Dilate the figure using center \(P\) and scale factor \(\frac12\).

- What do you notice? What do you wonder?

- Dilate segment \(AB\) using center \(P\) by scale factor \(\frac12 \). Label the result \(A'B'\).
- Dilate the segment \(AB\) using center \(Q\) by scale factor \(\frac12\).
- How does the length of \(A''B''\) compare to \(A'B\)? How would the length of \(A''B''\) change if \(Q\) was infinitely far away? Explain or show your answer.

### Summary

A scale drawing of an object is a drawing in which all lengths in the drawing correspond to lengths in the object by the same scale. When we scale a figure we need to be sure to scale all of the parts equally or else the image will become distorted.

Creating a scaled copy involves multiplying the lengths in the original figure by a **scale factor**. The scale factor is the factor by which every length in a original figure is multiplied when you make a scaled copy. A scale factor greater than 1 enlarges an object while a scale factor less than 1 shrinks an object. What would a scale factor equal to 1 do?

For example, segment \(BC\) is a scaled copy of segment \(DE\) with a scale factor of \(\frac14\). So \(BC=\frac14DE\). If \(DE=6\), then \(BC=\frac64\) or 1.5.

Segment \(FG\) is a dilation of segment \(DE\) using center \(A\) and a scale factor of 3. So \(FA=3 \boldcdot DA\). If \(DA=15\), then \(FA=45\).

### Glossary Entries

**dilation**A dilation with center \(P\) and positive scale factor \(k\) takes a point \(A\) along the ray \(PA\) to another point whose distance is \(k\) times farther away from \(P\) than \(A\) is.

Triangle \(A'B'C'\) is the result of applying a dilation with center \(P\) and scale factor 3 to triangle \(ABC\).

**scale factor**The factor by which every length in an original figure is increased or decreased when you make a scaled copy. For example, if you draw a copy of a figure in which every length is magnified by 2, then you have a scaled copy with a scale factor of 2.