Bell Work:Simplify

4.36 0.4

Answer:= 10.9

LESSON 26:TRANSFORMATIONS

Transformations*: operations on a geometric figure that alter its position or form.

There are 4 forms of transformations that we will be discussing today; reflection, rotation, translation and dilation.

Reflection*: a transformation by flipping a figure to produce a mirror image. Does not change the size of a figure.

Here we show a reflection of a triangle across the y-axis. Each point in the reflection is the same distance from the y-axis as the corresponding point in the original figure. Notice that if we were to fold this graph in half, the figures would coincide exactly.

Rotation*: a transformation by turning a figure about a specified point called the center of rotation. Does not change the size of a figure.

A positive rotation turns a figure counter-clockwise around a point. Here we show a 90 degree rotation around the origin. If we trace the path of this rotation, we find that it sweeps out an arc of 90 degrees.

Translation*: a transformation by sliding a figure from one position to another without turning or flipping the figure. Does not change the size.

Here we show a translation of (0, -9) which is 9 units down from the original figure. For any translation (x, y), x describes the horizontal shift and y describes the vertical shift.

Describe the transformations that move ΔABC to the location of ΔA’B’C’.

A

B CA’

B’

C’

We will use all three transformations. We begin by reflecting ΔABC across line AC.

A

BC

A’

B’

C’

Then we rotate ΔABC 90 degrees about point C.

A

B

CA’

B’

C’

We finish by translating ΔABC 8 units to the right and 1 unit up.

Reflection, rotation, and translation do not change the size of the figure. These transformations are called isometries or congruence transformations.

Dilation*: a transformation in which the figure grows larger. (a contraction is a transformation in which the figure grows smaller)

An example of a dilation is a photographic enlargement.

Although a dilation changes the dimensions of a figure, it does not change its shape. The original figure and its image are similar and corresponding lengths are proportional. Thus, dilations and contractions are similarity transformations.

Dilations of geometric figures occur away from a fixed point that is the center of the dilation.

Note that corresponding vertices are on the same rays from the center of dilation and that the corresponding segments of ΔABC and its image ΔA’B’C’ are parallel.

A B

C D

A’ B’

C’ D’

HW: Lesson 26 #1-30Due Tomorrow