1. I can draw dilations in the coordinate plane.

2. Math Shorts: Dilations

3. If the images to the right describe a translation, in your own words, define translation:

4. Dilations on a Coordinate Plane
Vocabulary!
Dilations on a Coordinate Plane
Scale Factor
A dilation or scaling is a similarity transformation
that enlarges or reduces a figure proportionally
with respect to a center point and a scale factor.
The ratio of a length on an image to a corresponding length
on the preimage.
To find the coordinates of an image after a dilation
centered at the origin, multiply the x- and y-coordinates
of each point on the preimage by the scale factor
of the dilation, k.
𝑥, 𝑦 → 𝑘𝑥, 𝑘𝑦

5. Example 1:
Trapezoid EFGH has vertices E(–8, 4), F(–4, 8), G(8, 4) and H(–4, –8). Graph the image of EFGH after a dilation centered at the origin with a scale factor of 1/4.
*Multiply the scale factor by each x and y coordinate to find the dilated image
𝐸 ′ −8∗ 1 4 , 4∗ 1 4 = 𝐸 ′ −2, 1
𝐹 ′ −4∗ 1 4 , 8∗ 1 4 =𝐹′(−1, 2)
𝐺 ′ 8∗ 1 4 , 4∗ 1 4 =𝐺′(2, 1)
𝐻 ′ −4∗ 1 4 , −8∗ 1 4 =𝐻′(−1,−2)

6. Example 2a:
Find the image of each polygon with the given vertices after a dilation centered at the origin with the given scale factor. J(2, 4), K(4, 4), P(3, 2); r = 2
𝐽 ′ 2∗2, 4∗2 = 𝐽 ′ 4, 8
𝐾 ′ 4∗2, 4∗2 = 𝐾 ′ 8, 8
𝑃 ′ 3∗2, 2∗2 =𝑃′(6, 4)

7. Example 2b:
Find the image of each polygon with the given vertices after a dilation centered at the origin with the given scale factor. D(–2, 0), G(0, 2), F(2, –2) r= 1.5
𝐷 ′ −2∗1.5, 0∗1.5 = 𝐷 ′ −3, 0
𝐺 ′ 0∗1.5, 2∗1.5 = 𝐺 ′ 0, 3
𝐹 ′ 2∗1.5, −1∗1.5 =𝐹′(3, −3)

8. Example 3:
Leila drew a polygon with coordinates (–1, 2), (1, 2), (1, –2), and (–1, –2). She then dilated the image and obtained another polygon with coordinates (–6, 12), (6, 12), (6, –12), and (–6, –12). What was the scale factor and center of this dilation?
𝑘𝑥, 𝑘𝑦 → 𝑥,𝑦
𝑘∗−1, 𝑘∗2 → −6, 12
𝑘∗−1=− 𝑘∗2=12
𝑘= 𝑘=6
Scale Factor = 6

9. Example 4:
Find the scale factor from the pre-image to the image for the following dilation. A(2,5), B(3,-1), C(4,2) and A’(3, 7.5), B’(4.5, -1.5), C‘(6, 3).
𝑘𝑥, 𝑘𝑦 → 𝑥,𝑦
𝑘∗2, 𝑘∗5 → 3, 7.5
𝑘∗2= 𝑘∗5=7.5
𝑘= 𝑘=1.5
Scale Factor = 1.5

10. Do the summary on your own!

11. Summary!
Nemo is located on the coordinate plane. Write down Nemo’s coordinate points here: Marlin believes Nemo will be 3 times the size he is now. Dilate the Nemo using a scale factor of 3. Write the coordinate points here: Graph the dilated coordinate points and name them accordingly. When you are finished, compare with your neighbor.