A scale tells how the measurements in a scale drawing represent the actual measurements.

The scale on this floor plan tells us that 1 inch on the drawing represents 8 feet in the actual room. This means that 2 inches represent 16 feet, and \(\frac12\) inch represents 4 feet.

A scale drawing represents an actual place or object. All the measurements in the drawing correspond to the measurements of the actual object by the same scale.

To create a scaled copy of a figure, all the side lengths in the original figure are multiplied by the same number. This number is called the scale factor.

In this example, the scale factor is 1.5, because \(4 \boldcdot (1.5) = 6\), \(5 \boldcdot (1.5)=7.5\), and \(6 \boldcdot (1.5)=9\).

A scaled copy is a copy of a figure where every side length in the original figure is multiplied by the same number.

Triangle \(DEF\) is a scaled copy of triangle \(ABC\). Each side length on triangle \(ABC\) is multiplied by 1.5 to get the corresponding side length on triangle \(DEF\).

Two figures are similar if one can fit exactly over the other after transformations.

This figure shows triangle \(ABC\) is similar to triangle \(DEF\).

• Rotate triangle \(ABC\) around point \(B\). 
• Then dilate it with center point \(O\).
• The image will fit exactly over triangle \(DEF\).

A sequence of transformations. Triangle ABC is rotated around point B and and then dilated with center point O to fit exactly over Triangle DEF. Triangle ABC is similar to triangle DEF.

Slope is a number that describes how steep a line is. To find the slope, divide the vertical change by the horizontal change for any 2 points on the line.

The slope of this line is 2 divided by 3, or \(\frac23\).