March 04, 2015
7.1 Rigid Motion in a Plane
Obj.: Identify the three basic rigid transformations.
Transformation - an operation that maps the preimage onto
the image.
Image - new figure resulting from transformation
Preimage - original figure
3 basic transformations:
1.
2.
3.
Isometry - preserves
lengths, ∠s, // lines (in
other words-->keeps the
same shape and size)
[Rigid Transformations]
EX:
EX:
2x
+5
Try this...solve for x.
March 04, 2015
7.2 Reflections
Obj.: Identify and use reflections in a plane.
*Act. p. 403
Reflection - a transformation that uses a line that acts
like a mirror.
2. If P is on m,
1. If P is not on m,
then m is the ⊥
m
then P=P'.
bisector of PP'.
Theorem 7.1 Reflection Thm. - A reflection is an isometry.
How do we construct them?
What do we need to describe them?
m
March 04, 2015
Ex: Graph the given reflections
a. G(2, 8) in the x-axis
b. H(-4, 5) in the y-axis
Notice any patterns?
Verify your conjecture.
If (x,y) is reflected in the x-axis,
then (x,y)
If (x,y) is reflected in the y-axis,
then (x,y)
Ex2: Graph the given reflections
a. J(4, -2) in the line x=5
b. K(-3, -6) in the line y=-2
x=a is the equation of a...
y=b is the equation of a...
March 04, 2015
Line of Symmetry - a line that allows a figure to be
mapped onto itself by a reflection in that line.
Ex3: Determine the number of lines of symmetry that each
of the pattern blocks have.
How about these flags?
Ex: The electric company is trying to find a location
along the street for a box that will minimize the
amount of wire they will need to hook up both
houses in the picture. Where should they put the
box?
This is a good one!
Electric Co.