A dilation is a transformation that can reduce or enlarge a figure. Each point on the figure moves along a line closer to or farther from a fixed point. That fixed point is the center of the dilation. All of the original distances are multiplied by the same scale factor.

Triangle is a dilation of triangle . The center of dilation is . The scale factor is 3.

Every point of triangle is 3 times as far from as every corresponding point of triangle .

Two numbers that multiply to equal 1 are reciprocals.

• 8 and are reciprocals because .
• is a reciprocal of because .

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  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 , , and .

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

Triangle is a scaled copy of triangle . Each side length on triangle is multiplied by 1.5 to get the corresponding side length on triangle .

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

This figure shows triangle is similar to triangle .

• Rotate triangle around point . 
• Then dilate it with center point .
• The image will fit exactly over triangle .

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 .