toc #4 scale factor

TOC #4 Scale Factor

Unit 5 – Staying in Shape

What is scale factor?

Scale factor:

- The ratio used to reduce or enlarge similar figures.

- The number we multiply an existing dimension or coordinate to find the

new dimension or coordinate.

What is a dilation?

Dilation:

- The type of transformation where a figure’s size is increased or decreased.

Scale factor < 100%reduces a figure

Less than 100% means multiplying by a number less than 1.

The new figure will be reduced in size.

Scale factor = 100%keeps a figure the same

Equal to 100% means multiplying by 1.

The figure will be the same or congruent.

Scale factor > 100%enlarges a figure

Greater than 100% means multiplying by greater than 1.

The figure will be enlarged or greater in size.

Using scale factor…example #1

A rectangle has a length of 4cm and a width of 3 cm. Find the new dimensions with a scale factor = 4.

Using scale factor…example #2

A triangle has a base of 4.5 cm. What is the length of its base with a scale factor of 5cm?

Using scale factor…example #3

A rectangle has a length of 12m and a width of 8m. What are the dimensions of a similar rectangle with a scale factor of 0.5?

Using scale factor…example #4

The coordinates of point A are at (4, 5). What would the new coordinates be after a scale factor of 3 is applied?

Scale factor and area

Given the two rectangles below, find the area of the first rectangle and then the area of the second.

2m 6m

3m x

Scale factor and area…

Original Figure

Length of

10 cm

Width of

6cm

Area of

60 sq cm

Scale factor of 3

Scale factor of 0.5

Scale factor of 1

Scale factor conclusions

The scale factor for AREA:

- The scale factor for the outside dimensions squared.

Unless it is specified, scale factor will refer to the ratio of the side lengths NOT the scale factor of the area.

Working backwards…If a rectangle has an area of 6 square units, and its copy has an area of 24 square units, find the scale factor.

1st find the scale factor of the area:

6 x ? = 24 ? = 4

2nd “un-square” it to find the scale factor for the figures dimensions.

4 = ? x ? Scale factor = 2

Homework…

Complete the handout

“Using Scale Factor”