- To transform a figure (shape) means changing the size, location, and direction it faces.
- The figure before the transformation is called the pre-image.
- The figure after the transformation is called the image.
- If the pre-image is labeled as A, then the image would be labeled as A' (pronounced as A prime).
- There are four different types of transformation.
- The image after the dilation is similar to the pre-image.
- Two images are similar if:
- They are of different sizes with proportional sides.
- All angles are congruent.
- They can be mapped on one another with a series of transformations.
- The symbol for similarity is ∼.
- A dilation is a type of transformation that resizes (stretches or shrinks) the original figure.
- A dilation produces an image that is the same shape as the original but different in size.
- Dilation produces similar but not congruent images.
- It enlarges or reduces the size of the original figure (pre-image) with a scale factor.
- A dilation needs a center point, also called as the center of dilation, and a scale factor.
- The center of dilation or the center point is a fixed point in the plane.
- The scale factor is a ratio of the corresponding sides in a figure.
- A scale factor between 0 and 1 means the resulting image will be shrunk/reduced.
- A scale factor > 0 means the resulting image will be enlarged.
- A scale factor of 1 means the pre-image and image are congruent.
Question 1: If the scale factor of a dilation centered at the origin is 3, find the image of the point (2, 7).
Solution: If the scale factor is , it follows the dilation rule .
Hence, the dilated image of the point (2, 7) will be .
Question 2: is plotted on the coordinate grid. If the figure were dilated by a scale factor with the origin as the center of dilation, what are the coordinates of the vertices of .
|Pre-image||Image after dilation|
Question 3: is the image of under a dilation with a scale factor of 4 as shown in the figure below. Find the length of segment .
- Look for keywords: Stretch, Enlarge, Reduce, and Shrink.
- In dilation, the figure stretches or shrinks based on a scale factor.
- where k is the scale factor.
- Dilated images are similar but not congruent.
- Differentiate between pre-image (A) and image (A').
- The scale factor in fractions does not always reduce the size of the figure.