Holt Geometry

1-7 Transformations in the Coordinate Plane

Warm Up

1. Which describes a translation?a) Turn b) Flip c) Slide

2. Which describes a rotation?a) Turn b) Flip c) Slide

3. Which describes a reflection?a) Turn b) Flip c) Slide

Holt Geometry

1-7 Transformations in the Coordinate Plane

Identify reflections, rotations, and translations.

Graph transformations in the coordinate plane.

Objectives

Holt Geometry

1-7 Transformations in the Coordinate Plane

transformation reflectionpreimage rotationimage translation

Vocabulary

Holt Geometry

1-7 Transformations in the Coordinate Plane

•A transformation is a change in the position, size, or shape of a figure.

•The original figure is called the preimage. The resulting figure is called the image.

•A transformation maps the preimage to the image.•Arrow notation () is used to describe a transformation, and primes (’) are used to label the image.

•An isometry transformation that does NOT change the size or shape or the preimage.

Holt Geometry

1-7 Transformations in the Coordinate Plane

Holt Geometry

1-7 Transformations in the Coordinate Plane

•Translations can be described by a rule such as (x, y) (x + a, y + b).

•To find coordinates for the image of a figure in a translation, add a to the x-coordinates of the preimage and add b to the y-coordinates of the preimage.

Holt Geometry

1-7 Transformations in the Coordinate Plane

Check It Out! Example 1

• Write a translation statement for the following transformation and name the image.

Translate the point A(4, -5) to the left 2 and up 7.

Translation statement: (__, __) → (_______, _______)

Plug in: A(4, -5) → (_______, _______)

Image: A’(___, ___)

x y x - 2 y + 7

4 - 2 -5 + 7

2 2

Holt Geometry

1-7 Transformations in the Coordinate Plane

Translations using vector notation

A vector is a set of directions telling a point howto move.

- Denoted with angle brackets < x, y > -Tells movement in x direction, then y direction

Example: Move point A along the vector <__, __>-2 7

Holt Geometry

1-7 Transformations in the Coordinate Plane

Your Turn!

1. Translate R(3, 7) to the right 4 and up 3

Translation statement: (__, __) → (_______, _______)

Image: ____(___, ___)

x y x + 4 y + 3

7 10

• Write a translation statement for the following transformation and name the image.

R’

2. Translate U(-6, 3) along the vector <2, -5>

Translation statement: (__, __) → (_______, _______)

Image: ____(___, ___)

x y x + 2 y – 5

-4 -2U’

Holt Geometry

1-7 Transformations in the Coordinate Plane

Whiteboard Problems: 1

A(–2, –4)

B(–1, –2)

C(–3, 0)

A’(0, 0)

B’(1, 2)

C’(–1, 4)

Find the coordinates for the image of ∆ABC after the translation (x, y) (x + 2, y + 4). Draw the image.

A

B

C

A’

B’

C’

Holt Geometry

1-7 Transformations in the Coordinate Plane

Whiteboard Problems: 2

R(–4, –4)

S(–2, –3)

T(–1, 3)

R’(1, –4)

S’(3, –3)

T’(4, 3)

Find the coordinates for the image of ∆RST after the vector <5,0>. Draw the image.

RS

T

R’S’

T’

Holt Geometry

1-7 Transformations in the Coordinate Plane

Whiteboard Problems: 3

K(2, 6)

I(4, 2)

T(-2, 4)

E(8, 4)

K’(-4, 0)

I’(-2, -4)

T’(-8, -2)

E’(2, -2)

Find the coordinates for the image of KITE if it moved down 6 and to the left 6. Write the translation statement and the vector. Draw the image.

Translation statement:

(x, y) → (x – 6, y – 6)

Vector: <-6, -6>

K

I

T E

K’

I’

T’ E’

Holt Geometry

1-7 Transformations in the Coordinate Plane

Holt Geometry

1-7 Transformations in the Coordinate Plane

Check It Out! Example 1

Identify each transformation. Then use arrow notation to describe the transformation.

translation; MNOP M’N’O’P’ rotation; ∆XYZ ∆X’Y’Z’

a. b.

Holt Geometry

1-7 Transformations in the Coordinate Plane

Check It Out! Example 2

A figure has vertices at E(2, 0), F(2, -1), G(5, -1), and H(5, 0). After a transformation, the image of the figure has vertices at E’(0, 2), F’(1, 2), G’(1, 5), and H’(0, 5). Draw the preimage and image. Then identify the transformation.

Plot the points. Then use a straightedge to connect the vertices.

The transformation is a 90° counterclockwise rotation.

Holt Geometry

1-7 Transformations in the Coordinate Plane

Check It Out! Example 4

Use the diagram to write a rule for the translation of square 1 to square 3.

Step 1 Choose two points.

Choose a Point A on the preimage and a corresponding Point A’ on the image. A has coordinate (3, 1) and A’ has coordinates (–1, –3).

A’

Holt Geometry

1-7 Transformations in the Coordinate Plane

Check It Out! Example 4 Continued

Use the diagram to write a rule for the translation of square 1 to square 3.

Step 2 Translate.

To translate A to A’, 4 units are subtracted from the x-coordinate and 4 units are subtracted from the y-coordinate. Therefore, the translation rule is (x, y) (x – 4, y – 4).

A’