\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)

Enlargement and Reduction

Definitions


Look at the rectangles below. They have the same shape but different sizes because their side lengths grow or shrink by the same multiplier.
Rectangle \( A \) is enlarged to \( A' \) by doubling its side lengths (multiplying by 2). Notice how the width and height both double.

Definition Enlargement and Reduction
  • An enlargement makes a shape larger by multiplying all side lengths by a number called the scale factor.
    In this example, shape \( A \) is enlarged to \( A' \) by multiplying side lengths by \(\textcolor{olive}{2}\) (scale factor = \(\textcolor{olive}{2}\)). The bottom side grows from 4 to 8 squares.
  • A reduction makes a shape smaller by dividing all side lengths by a number called the scale factor.
    In this example, shape \( A \) is reduced to \( A' \) by dividing side lengths by \(\textcolor{olive}{2}\) (scale factor = \(\textcolor{olive}{2}\)). The bottom side shrinks from 8 to 4 squares.