TCP - Dilations Lesson

Dilations

A dilation is a transformation that maintains the original shape of the figure, but stretches or shrinks the size. All of our dilations will use the origin, (0, 0) as the center of dilation.

Let's start with this square. Notice that all of the sides have a length of 2 units.

graph of box with a length of 2 units

Now, let's dilate the figure by a scale factor of 3. We can notate this dilation by equation image indicator $LaTeX: \left(3x,\:3y\right)$ $\left(3x,\:3y\right)$

graph of original box that has been dilated to a length of 6 units; "Because the scale factor is greater than 1, we consider this to be a STRETCH."

Now, let's dilate the figure by a scale factor of 1/2. We can notate this dilation by equation image indicator $LaTeX: \left(\frac{1}{2}x,\:\frac{1}{2}y\right)$ $\left(\frac{1}{2}x,\:\frac{1}{2}y\right)$

graph of a box with a length of 1 unit; "Because the scale factor is less than 1, we consider this to be a SHRINK."

Let's try another dilation.

Original:
C: (-2,-1)
D: (-1, 2)
E: (3,1)
Dilated:
C:(-4,-2)
D:(-2,4)
E:(6,2)

Question: How did the ordered pairs in the dilation above change?

Solution: The x's and y's have all been multiplied by 2

Properties preserved when an object is Dilated:
1. Angles: The angle measures do not change!
2. Parallel and perpendicular lines remain parallel and perpendicular!
3. Midpoints: Midpoints of segments do not change!
4. Orientation: The order of the letters will not change
When an object is dilated the DISTANCES are changed: the length of line segments either increases or decreases.

Watch this video to practice a few more problems:

Dilations Practice

IMAGES CREATED BY GAVS USING FREE PSD