Lesson 11.4Translations and Reflections

Translation - Each point of a figure is moved in the same distance in the same direction (sometimes called as slide).

Image- the figure you get after the transformation . The translation of A to its image is A’.

Example of Translation

Example of Translation

Notation ( )

A point and its image after a translation are given. Write a rule to describe the translation•A(9,-4), A’(2,1)

•B(-3, 5), B’(-5,-3)

( , ) ( 7, 5)x y x y

( , ) ( 2, 8)x y x y

The triangle below is translated 5 units right and4 units down. Describe the translation below using a coordinate table.

y

x

D

CE

+5

-4

C

D

E

Understanding Translation

Coordinate Table

x y-5 1-2 40 2

x+5 y-40 -33 05 -2

CDE

Reflection

• Mirror image either over the x or y axis

Rule for Line Reflection Over Y-axis

'( , ) ( , )A x y A x y

y

x

Reflect ABC over the y-axis.

A

BC

Coordinate NotationA

BC

Line ReflectionsLine Reflection - Reflection occurs when points are redrawn across a line of symmetry at equal distance.

x y-5 4-5 1-1 1

-x y5 45 11 1

“Opposite of”

Reflect over Y-AXIS (-x, y) – opposite of x

Reflect over X-AXIS (x, -y) – opposite of y

Rule for Line Reflection over x-axis

( , ) '( , )A x y A x y

Points L(-3,2), M(3,1), and N(-2,-2) are the vertices of a triangle. If LMN is reflected over the x-axis,what are the coordinates of its image?

y

x

LM

N

Coordinate Notation

M

N

L

Homework

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