Geometry/Trig
Name:
Date:
Lesson 9-12 Dilations
Learning Goal: What type of transformation is dilation?
How do we perform dilations of points and geometric figures?
Individual Activity:
1. Given triangle ABC with vertices A(2, 4) B(4, 4) and C(4, 2):
a. Plot the pre-image
b. Multiply each coordinate of the vertices of triangle ABC (both x and y) by 3, and plot your new points.
i. State the coordinates of your new points
ii. How are triangle ABC and your new triangle related? What other observations did you make?
1
c. Multiply each coordinate (both x and y) of the vertices of triangle ABC by 2, and plot your new points.
i. State the coordinates of your new points.
ii. How are triangle ABC and
your new triangle related?
What other observations did
you make?
Geometry/Trig
Dilations
Vocab to Know about Dilations
Term
Definition
A transformation that ___________________
or _______________ the size of a geometric
figure
Used to measure the distances to the preimage and the dilation image. The point a preimage in a dilation expand/shrinks from
Ratio of the distance/length of the image over
the pre-image
Typically uses the symbol, k.
Facts to Know about Dilations
* The center of dilation, a pre-image point, and its corresponding image points are all _____________________.
This means that they are ________________________________________.
*The notation for dilation is: ____________ *Center of dilation will always be at (0,0) for our examples!
Let’s Start With Similarity
Compare it!
The following figures are similar. Use this to come up with your own
definition of what it means for figures to be similar.
Think out Loud: What do you think it means for geometric figures to be "Similar"?
Notation:
Geometry/Trig
New Vocab Alert!!
Scale Factor!
K=
1. Our task: Determine the scale factor of the following dilation:
a) Did the figure get bigger or smaller? How do you know?
b) What is the scale factor?
Think about it!
Using your “Individual Activity” and the above
questions, what can we conlcude?
When the dilation made the pre-image bigger, the scale factor was ____________________ than one.
Vs.
When the dilation made the pre-image smaller, the scale factor was _______________________ than one.
Dilating a figure on the coordinate plane
Graph △PQR with vertices P (0, 2), Q (1, 0), and R (2, 2) and its image after a dilation with scale factor 3
and a center of dilation at point (0, 0).
Procedure:
1. Plot pre-image
and center of
dilation
2. Multiply the (x,y)
of each vertex by
scale factor
3. Plot the new
points!
State
the points of the image, and plot them.
P’ _______
Q’ _______
R’ _______
Geometry/Trig
Try one!
Triangle ABC is shown in the figure. Find the vertices and graph of the triangle under dilation with a scale factor 2
centered at (0,0).
*Perfect Practice Makes Perfect!
1. (a) On the accompanying set of axes, graph ΔABC with coordinates A(-4,4), B(0,2), and C(1,8).
(b) Then, state the coordinates of ΔA'B'C' and graph the image of ΔABC after 𝐷2 centered at the origin.
Geometry/Trig
2. Quadrilateral ABCD has vertices
,
,
, and
. Graph and state the coordinates of
, the image of quadrilateral ABCD under a dilation of factor
3. Under a dilation where the center of dilation is the origin, the image of
coordinates of , the image of
under the same dilation?
is
. What are the
Hint! We might need to work
backwards for this one!
4. Triangle ABC has vertices
,
State and label the coordinates of
after a dilation of
.
, and
.
Geometry/Trig
5.
Pentagon ABCDE has vertices A(0,0), B(3,3), C(6,3), D(6,-3) and E(3,-3).
a. Graph ABCDE
b. Graph A’B’C’D’E’ when the following transformation is performed: D1/3
A(0,0)
A’ (
)
B(3,3)
B’ (
)
C(6,3)
C’ (
)
D(6,-3)
D’ (
)
E(3,-3)
E’ (
)