Scale Factor

1
Scale Factor

• M7G3 Students will use the properties of
  similarity and apply these concepts to geometric
  figures.

2
Scale Factor (Using Rules)

• (x, y)
• A rule is applied to a coordinate pair to enlarge
  or shrink a shape and to translate a shape to a
  new position.

Multiply

• Multiply x and y by a whole number will enlarge
  the shape.
• Multiply x and y by a fraction will shrink the
  shape.
• Multiply a number with x and the width will
  change.
• Multiply a number with y and the height will
  change.

Add

• Adding or subtracting a number to x and y will
  change the location of the shape on the
  coordinate graph.
• Adding to x moves the shape to the right.
• Subtracting from x moves the shape to the left.
• Adding to y moves the shape up.
• Subtracting from y moves the shape down.

3
Rule Examples

• Explain what would happen to a figure if you
  transformed it using the given rule.
• (15x, 20y)
• (3x, 9y 5)
• (x 4, 4y)
• (6x 7, 6y 2)
• (¼x, ¼y)

4
Scale Factor

• The ratio of corresponding side lengths. The
  number that is multiplied by the side lengths to
  produce a new shape.

Ratio

• A comparison of two quantities, usually expressed
  as a fraction.

Corresponding Side Lengths

• Side lengths in two different shapes that are in
  the same position.

Corresponding Angles

• Angles in two different shapes that are in the
  same position.

Similar Figures

• Two shapes that have the same shape but not the
  same size.

5
How to find Scale Factor

• When a figure is dilated, its size is changed by
  multiplying the length of each side by a scale
  factor.  All angles remain the same and so the
  new shape (or image) is similar to the original.
• Can be found by dividing a new side length by the
  original side length.

• When going from a small shape to a larger shape
  the scale factor is greater than 1.

• When going from a large shape to a smaller shape
  the scale factor is less than 1.

1. Determine the corresponding side lengths.
2. Determine if you are making a larger shape or a
   smaller shape.
3. Determine if the scale factor is greater than or
   less than 1.
4. Right the correct ratio.

6
How is the perimeter and area of a figure
affected by the scale factor?

• Perimeter Scale Factor is the same as the scale
  factor.
• Area Scale Factor is the scale factor squared.