1. Dilation is a transformation that changes the size of a figure by a scale factor relative to a fixed point, called the center of dilation. If the scale factor is greater than 1, the figure enlarges; if it is between 0 and 1, the figure shrinks. The shape and orientation remain the same.
2. To find the coordinates of a dilated image:
- Identify the center of dilation (often the origin unless specified otherwise).
- Multiply both the x-coordinate and y-coordinate of each vertex of the original figure by the given scale factor.
- Plot the new points to form the dilated image.
3. Yes, it is possible to have more than one correct answer for the scale factor if the problem does not specify whether the dilation is an enlargement or reduction, or if the center of dilation is not fixed. For example, a figure could be dilated by a scale factor of 2 (enlargement) or 1/2 (reduction) to produce similar figures, depending on context.
4.
- Original triangle vertices: A(2, 2), B(4, 2), C(3, 5)
- Scale factor: 2
- New coordinates: A'(4, 4), B'(8, 4), C'(6, 10)
5.
- Original square vertices: P(-2, -1), Q(1, -1), R(1, 2), S(-2, 2)
- Scale factor: 0.5
- New coordinates: P'(-1, -0.5), Q'(0.5, -0.5), R'(0.5, 1), S'(-1, 1)
Parent Tip: Review the logic above to help your child master the concept of dilation translation worksheet.
