6th Grade Math Textbook, Fundamentals

 &KDSWHU

13-10

Graph Translations and Reflections

Objective To demonstrate the reflection or translation of points on a coordinate plane

• To identify the reflection or translation of polygons on a coordinate plane • To graph
  the reflection or translation of polygons on a coordinate plane

Ms. Choi is stenciling a simple border of a repeating kite-

pattern along the wall near the ceiling. Does the border

represent a translation or a reflection pattern?

A is a change in orientation (position),

shape, or size of a figure. The figure that results from a

transformation is called the. Using prime notation,

the image of a point Pis identified as P′and is read as

“P prime.”

A is a transformation that slides every point of a

figure the same distance and in the same direction along a

straight line without turning. In a translation, the figures are

congruent and the orientation stays the same.

A is a transformation that flips a figure over a line.

This line is called the. In a reflection, the image

is congruent to the original, but has a different orientation.

Ms. Choi’s pattern represents a translation, because the figure

slides along a straight line without turning and all

corresponding angle measures and segment lengths in the

image are congruent to the original.

Points can also be transformed on a coordinate plane.

• Translate point P(1, 1) four units to the right and two
  units up. What are the coordinates of P′?
  Locate point P. Then from point Pmove 4 units right
  and 2 units up. Plot P′.
  P′(3, 3)


• Reflect point P(1, 1) over the x-axis.
  Reflect point R(3, 2) over the y-axis.
  What are the coordinates of P′and R′?
  To reflect a point over the x-axis, use the same x-coordinate
  and multiply the y-coordinate by 1. Plot P′.
  P′(1, 1)
  To reflect a point over the y-axis, use the same y-coordinate
  and multiply the x-coordinate by 1. Plot R′.
  R′(3, 2)

image

line of reflection

reflection

translation

transformation

In a reflection, the

figure and the image

are mirror images of

each other and the

line of reflection is a

line of symmetry.

0

y

x

 1 14562 3

 2

 3

 4

1

2

3

4

 4  3  2  1

P‘

P

2 units up

(3,3)

4 units right

0

y

x

 1 142 3

 2

 3

 4

1

2

3

4

 4  3  2  1

P

R

P‘

R‘