Download Congruence and Transformations

CONGRUENCE AND
TRANSFORMATIONS
SECTION 4.4
Plot the following points on the coordinate plane:
Label each point.
A (0,3)
B(2,4)
C(-2,0)
C(-3,-5)
E(4,-2)
A transformation is a change in the
position or size of a figure.
Some transformations are:
• Translations (slides)
• Reflections (flips)
• Rotations (turns)
• Dilations (changes size)
• An Isometry or rigid
transformation is a
transformation that
preserves length, angle
measure and area.
The image is congruent
to the pre-image.
• Translations,
reflections, and
rotations are all rigid
transformations. The
image is CONGRUENT
to the pre-image.
• A dilation changes the
image with a scale
factor so this is not a
rigid transformation.
The image is SIMILAR
to the pre-image.
DILATION
IF YOU ENLARGE THE IMAGE, THE
SCALE FACTOR IS GREATER THAN ONE.
IF YOU REDUCE THE IMAGE, THE SCALE
FACTOR IS LESS THAN ONE.
Apply the transformation M to the polygon with the given
vertices. Then identify and describe the transformation.
1.
M: (x,y)
(x+2, y – 5)
P(1,2), Q(4,4), R(4,2)
2.
M: (x,y)
(-x,y)
A(1,1), B(3,2), C(3,5)
3. M: (x,y)
(-y,x)
R(1,2), E(1,4), C(5,4), T(5,2)
4.
M: (x,y)
(2x,2y)
K(-1,2), L(2,2), N(1,3)
Determine whether the figures are congruent.
Then state the type of transformation and describe it.
Give the rule.
1. A(1,1), B(4,1), C(4,3) vs.
P(-4,2), Q(-1,2), R(-1,4)
1. A(2,2), B(-4,4), C(2,4) vs.
P(3,3), Q(-6,6), R(3,6)
3. A(2,-1), B(3,0), C(2,3)
P(1,2), Q(0,3), R(-3,2)
vs.
4. A(-2,-2), B(-4,-1), C(-1,-1) vs.
T(2,2), U(4,1), V(1,1)
5. A(-4,4), B(-4,6), C(2,6), D(2,4) vs.
W(-2,2), x(-2,3), Y(1,3), Z(1,2)