11-4 Transformations in the Coordinate Plane

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

11-4 Transformations in the Coordinate Plane

Warm UpPlot the ordered pairs on the coordinate plane. Connect the points.

1. (3, 4)2. (–5, 0)3. (–2, 0)4. (–5, 4)

5. name the polygontrapezoid

x

y

2

0 2

-2

-2

4

4-4

-4

11-4 Transformations in the Coordinate Plane

Problem of the Day

Which capital letters of the alphabet have line symmetry?

A, B, C, D, E, H, I, K, M, O, T, U, V, W, X, Y

11-4 Transformations in the Coordinate Plane

Learn to use translations, reflections, and rotations to change the positions of figures in the coordinate plane.

11-4 Transformations in the Coordinate Plane

Additional Example 1: Translating Figures in the Coordinate Plane

Translate rectangle ABCD 4 units left. Give the coordinates of each vertex in the image.

Each vertex is translated 4 units right.

x

y

2

2

–2

–4

4

4

–4

–2 The vertices of the image are A’(–3, 2), B’(–1, 2), C’(–3, 1), and D'(–1, 1).

A B

C D

A’ B’

C’ D’

11-4 Transformations in the Coordinate Plane

A' is read “A prime.” Prime notation is used to represent the point on the image that corresponds to the same point on the original figure.

Reading Math

11-4 Transformations in the Coordinate Plane

Check It Out: Example 1

Translate square ABCD 5 units right. Give the coordinates of each vertex in the image.

Each vertex is translated 5 units right.

x

y

2

2

–2

–4

4

4–2

DC

BAThe vertices of the image are A’(–4, 1), B’(–1, 1), C’(–4, –4), and D'(–1, –4).

A' B'

C' D'

11-4 Transformations in the Coordinate Plane

Additional Example 2: Reflecting Figures in the Coordinate Plane

x

y

T

R

4

4

–4

Reflect triangle RST across the y-axis. Give the coordinates of each vertex in the image.

Each vertex of the image is the same distance from the y-axis as the corresponding vertex in the original figure.The vertices of the image are R’(–1, 0), S’(–2, 2), and T’(–2, –2).

S

T’

R’

S’

11-4 Transformations in the Coordinate Plane

A line of reflection is not limited to the x-axis or y-axis. Any line can be a line of reflection.

Helpful Hint

11-4 Transformations in the Coordinate Plane

Check It Out: Example 2

x

y

A

B

C

3

–3

Reflect triangle ABC across the x-axis. Give the coordinates of each vertex in the image.

Each vertex of the image is the same distance from the y-axis as the corresponding vertex in the original figure.The vertices of the image are A’(1, 0), B’(3, –3), and C’(5, 0).

A’

B’

C’

11-4 Transformations in the Coordinate Plane

Rotate triangle JKL 90° counter-clockwise about the origin. Give the coordinates of each vertex in the image.

Additional Example 3: Rotating Figures in the Coordinate Plane

Notice that the vertex K is 3 units to the right of the origin, and vertex K is 3 units above the origin.Similarly, vertex L is 1 unit to the right of the origin, and vertex L' is 1 unit above the origin.

x

y

2

–2

K'

J'

L'

J

KL–2 2

The vertices of the image are J’(–2, 2), K’(0, 3), and L’(0, 1).

11-4 Transformations in the Coordinate Plane

Rotate triangle JKL 180° counter-clockwise about the origin. Give the coordinates of each vertex in the image.

Check It Out: Example 3

The vertices of the triangle are ADC are A’(–3, –1), D’(0, 0), and C’(2, –2).

Notice that the vertex D’ remains on the origin.

11-4 Transformations in the Coordinate Plane

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

11-4 Transformations in the Coordinate Plane

Lesson Quiz

1. Translate triangle DEF down 5 units. Give the coordinates of each vertex in the image.

2. Reflect triangle DEF across the y-axis. Give the coordinates of each vertex in the image.

3. Rotate triangle DEF 90 clockwise around the origin. Give the coordinates of each vertex in the image.

D ’(1, –1), E ’(3, –3), F ’(2, –4)

D ’(– 1, 4), E ’(– 3, 2), F ’(–

2, 1)

D ’(4, –1), E ’(2, –3), F ’(1, –2)

11-4 Transformations in the Coordinate Plane

1. Describe the transformation.

A. translation 3 units up

B. translation 3 units down

C. reflection 3 units down

D. reflection 3 units up

Lesson Quiz for Student Response Systems

11-4 Transformations in the Coordinate Plane

2. Give the coordinates of each vertex after translated 2 units down.

A. A’(–4, 2), B’(–2, 2), C’(–3, 1)

B. A’(–4, 2), B’(–2, 2), C’(–3, –1)

C. A’(4, 2), B’(2, 2), C’(–3, 1)

D. A’(4, 2), B’(2, 2), C’(3, 1)

Lesson Quiz for Student Response Systems

11-4 Transformations in the Coordinate Plane

3. Give the coordinates of each vertex after reflected across the y-axis.

A. A’(4, –4), B’(2, –4), C’(3, –1)

B. A’(–4, –4), B’(–2, –4), C’(–3, –1)

C. A’(4, 4), B’(2, 4), C’(–3, 1)

D. A’(4, 4), B’(2, 4), C’(3, 1)

Lesson Quiz for Student Response Systems