Warm-Up
BellExercises
Work
Give the coordinates of a point twice as far from the
origin along a ray from (0, 0).
1. (3, 5)
2. (–2, 0)
Give the coordinates of a point one-half as far from the
origin along a ray from (0, 0).
3. (6, –4)
4. (0, –7)
Warm-Up1Exercises
EXAMPLE
1) Draw quadrilateral ABCD with vertices
A(3, 1), B(5, 1), C(5, – 1), and D(2, – 1).
2) Draw a dilation of ABCD. Use a scale factor of ½.
Warm-Up
Exercises
Notes
Definitions
Dilation
A transformation that stretches or shrinks a figure to create a
similar figure. It is a type of similarity transformation.
A figure is enlarged or reduced with respect to a fixed point
called the center of dilation. (ours will also be the origin)
The scale factor of a dilation is the ratio of a side length of the
image (end figure) to the corresponding side length of the
original figure.
Warm-Up2Exercises
EXAMPLE
1) Draw a triangle with vertices A(-1,– 1), B(1, -1), and
C(1,2).
2) Draw the image of triangle ABC after a dilation with
a scale factor of 3 . Call this triangle DEF.
3) Verify that
ABC and
DEF are similar.
Warm-Up
Exercises
Notes
Dilation
You can describe a dilation with respect to the origin with the
notation (x,y)
(kx, ky) where k is the scale factor.
If _____________, the dilation is an enlargement.
If _____________, the dilation is a reduction.
Warm-Up
Exercises
GUIDED
PRACTICE
Find the coordinates of L, M, and N so that LMN
is a dilation of PQR with a scale factor of k.
Sketch PQR and LMN.
P(–2, -1), Q(–1, 0), R(0, –1); k = 4
Warm-Up
Exercises
GUIDED
PRACTICE
Find the coordinates of L, M, and N so that LMN
is a dilation of PQR with a scale factor of k.
Sketch PQR and LMN.
P(5, –5), Q(10, –5), R(10, 5); k = 0.4
Warm-Up3Exercises
EXAMPLE
You want to enlarge a picture. Your photo is 4 inches
by 6 inches. You want a 24 x 36 print. What is the
scale factor of the dilation?
Warm-Up4Exercises
EXAMPLE
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
1.
Draw a dilation with scale factor 2 of ABC with
vertices A(1,0), B(0,3) and C(3,2). Label the image
DEF.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
2.
ABC has vertices A(0,0), B(0,8) and C(6,0). Draw a
dilation of ABC using a scale factor of 1 . Label
2
the image DEF.
ANSWER
Warm-Up
Quick Exercises
Check
Draw a shape with at least five sides.
Pick a scale factor for the dilation.
Switch papers and have the person sitting next to you
draw the image.
Switch back and check their work.
Warm-Up
Exercises
For Tomorrow
Homework
HW: 6.6 (pg. 406-407) #5,6,11,12,16-18