Examples:

• If the scale factor is $3$, the new shape will be three times as large.
• If the scale factor is $1/2$, the new shape will be half the size of the original

Worked Example 1: Enlarging a Shape

Given:

• Centre of Enlargement: ($-8, -6$)
• Scale Factor: $2$ Steps:

1. Draw lines from the centre of enlargement through each vertex (corner) of the blue object.
2. Measure the distance from the centre of enlargement to each vertex of the blue shape.
3. Double the distance to find where the vertices of the purple shape should be, as the scale factor is $2$.
4. Plot the new points and draw the enlarged purple shape. Notice: The distance of each point in the purple shape from the centre of enlargement is twice that of the corresponding point on the blue shape.

Worked Example 2: Reducing a Shape (Fractional Scale Factor)

Given:

• Centre of Enlargement: ($-6, 5$)
• Scale Factor: $1/3$ Steps:

5. Draw lines from the centre of enlargement through each vertex of the blue object.
6. Measure the distance from the centre of enlargement to each vertex of the blue shape.
7. Reduce the distance by a factor of $1/3$ to find where the vertices of the purple shape should be.
8. Plot the new points and draw the reduced purple shape. Notice: Since the shape got smaller, the scale factor is fractional (less than $1$). Each point on the purple shape is one-third the distance from the centre of enlargement as the corresponding point on the blue shape.