1. Lesson 9-R
Chapter 9 Review

2. Objectives
Review chapter 4 material

3. Vocabulary
None new

4. Reflections - Flips Equal distance from line of reflection
Origin (x,y)  (-x, -y) Multiply both by (origin is midpoint of all points and their primes)
Lines
1) x-axis (x,y)  (x, -y) Multiply y by -1 (line y=0 acts as midpoint of all points and primes)
2) y-axis (x,y)  (-x, y) Multiply x by -1 (line x=0 acts as midpoint of all points and primes)
3) line y = x (x,y)  (y, x) Switch x and y values (line y=x acts as midpoint of all points and primes)
4) horizontal line (y=k) similar in concept to x-axis, but no formula
5) vertical line (x=k) similar in concept to y-axis, but no formula

5. Translations - Slides
Transformation that moves all points of a figure, the same distance and direction
Translation function is the math effects or an equation relating old and new
Axis
Words
Math Effects Y Up
y’ = y + a
Down
y’ = y - a X
Right
x’ = x + a
Left
x’ = x - a
Don’t get fooled by order of appearance – focus on the words
Down 3 and right 4
(x + 4 , y – 3)
(x, y)  (x + 4, y - 3) Translation function

6. Rotations - Turns
A 180° rotation around the origin is the same as a reflection across the origin
90° rotations around the origin can be done by measuring how far the point is from the closest axis. Use that distance to tell you how far away from the new axis the new point is
Remember the second grade method
Other rotations require trig to figure out changes based on rotational angle and point of rotation

7. Tessellation - Covering
Pattern using polygons that covers a plane so that there are no gaps or overlaps at a vertrex
Gaps occur if angles sum to less than 360°
Overlaps occur if angles sum to more than 360°
Only regular polygons that tessellate are triangles, squares and hexagons.

8. Dilations – Shrinks & Expansions
All dilations are similar figures
New point locations can be found graphically by drawing lines through endpoints and the center point and measure distance from center point
negative values for r mean the figure is on the opposite side of the center point
CT – congruence transformation
Scaling Factor r
k< -1
k = -1
k > -1
k< 1
k = 1
k > 1
Expansion CT
Reduction
Larger figure
Flips
Smaller figure
No change
Opposite side of center point
Same side of center point
Effects

9. Misc Symmetry Lines of symmetry allow you to fold a figure in half
A regular figure has the same number of lines of symmetry as it has sides
Rotational symmetry – a figure can be rotated less than 360° so that the pre-image and image look the same (indistinguishable)
Order – number of times figure can be rotated less than 360° in above (# of sides in a regular polygon)
Magnitude – angle of rotation (360° / order)
Point of Symmetry: midpoint between an point and its “folded” point
exists for regular, even sided polygons
Does the figure look exactly like it started, with a 180° rotation

10. Vectors Vector notation <x,y> vs Point notation (x,y)
Vector length – magnitude = √x² + y²
Vector direction – angle = tan (y/x)
Scalar multiplication: distribute constant k<x,y> = <kx,ky>
Vector addition: add components <a,b> + <c,d> = <a+c,b+d> y x
Example: point (4,3) is the dot (white)
vector <4,3> is the diagonal line (red)
its x-component vector is the 4 part (yellow)
its y-component vector is the 3 part (orange)
Magnitude = √4² + 3² = 5
Direction: angle = tan (3/4) ≈ 37°

11. Summary & Homework Summary: Homework:
Translations, rotations and reflections are congruence transformations
Dilations
Are similar transformations
Are congruence transformations only for |r| = 1
Lines of symmetry divided a figure in half
Tessellations are like tiles on the floor
Homework:
study for the test