identifying combined transformations 5-8 warm up warm up lesson presentation lesson presentation...

Identifying Combined Transformations5-8

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


1. Original: A(-2, -1), B(-2, 1), C(1, 1), D(1, -1) Image : A'(-4, -2), B'(-4, 2), C '(2, 2), D'(2, -2)

2. Original: A(1, 1), B(1, 4), C(5, 1) Image : A'(1, -1), B'(1, -4),C '(5, -1)

Dilation; similar

Reflection; congruent

Warm UpIdentify each transformation from the original to the image, and tell whether the two figures are similar or congruent.


Problem of the DayA football field is in the shape of a rectangle with a length of 360 feet and a width of 160 feet. If a coach is drawing a football field on a chalkboard and has made a 54-cm line for the length, howlong should the line for the width of the field be?

24 cm


Learn to identify the image of a figure after a combined transformation is performed, anddetermine whether the final image is similar or congruent to the original.


Many famous geometric designs are created by combining transformations of various geometric figures.The mysterious crop circles shown here appear to be composed of combined rotations and dilations. If you consider the one piece that is rotated to create the design, you can see that it is similar to each of itsrotations.

Identifying Combined Transformations5-8Additional Example 1: Transformation Sequences and

CongruenceIdentify the combined transformations from the original to the final image, and tell whether the two figures are similar or congruent.Original : A(1, 1), B(2, –1), C(3, –5), D(2, –5)First Image: A'(1, 1), B'(2, 1), C'(3, 5), D'(2, 5) Final Image: A"(–3, –2), B"(–2, –2), C"(–1, 2), D"(–2, 2)

The original image to the first image: Reflection across x-axisThe first image to the final image: Translation 4 units left and 3 units downThe two figures are congruent.

Identifying Combined Transformations5-8Check It Out: Example 1

Original: A(2, –1), B(4, –1), C(5, –5), D(3, –5)First Image: A'(2, 1), B'(4, 1), C'(5, 5), D'(3, 5) Final Image: A"(–5, –5), B"(–3, –5), C"(–2, –1), D"(–4, –1)

The original image to the first image: Reflection across x-axisThe first image to the final image: Translation 7 units left and 6 units downThe two figures are congruent.

Identify the combined transformations from the original to the final image, and tell whether the two figures are similar or congruent.

Identifying Combined Transformations5-8Additional Example 2: Transformation Sequences and

SimilarityIdentify the combined transformations from the original to the final image, and tell whether the two figures are similar or congruent.

Original : A(1, 0), B(3, 1), C(4, –1), D(2, –2)First Image: A'(–1, 0), B'(–3, –1), C'(–4, 1), D'(–2, 2) Final Image: A"(–0.5, 0), B"(–1.5, –0.5),C"(–2, 0.5),D"(–1, 1)

The first image to the final image: dilation with scale factor of 0.5

The two figures are similar.

The original image to the first image: Rotation of 180 around origin


The original image to the first image: Translation3 units left and 2 units down

The first image to the final image: dilation with scale factor of 2

The two figures are similar.

Check It Out: Example 2


Identifying Combined Transformations5-8Additional Example 3: Finding Sequences of

TransformationsFind a sequence of at least two combined transformations from the original to the final image. Justify your answer.Original : A(–5, 1), B(–2, 4), C(–1, 1)Final Image: A"(1, –5), B"(4, –2), C"(1, –1)

Reflection across the x-axis; rotation of 90 counter-clockwise around the origin.


Reflection across the x-axis; translation 1 unit up

Check It Out: Example 3

Find a sequence of at least two combined transformations from the original to the final image. Justify your answer.Original : A(–5, 1), B(–2, 4), C(–1, 1)Final Image: A"(–5, –1), B"(–2, –4), C"(–1, –1)


Lesson Quizzes

Lesson Quiz for Student Response Systems

Standard Lesson Quiz


Lesson Quiz : Part-I


1. Original Δ ABC: A(1, 2), B(3, 4),C(3, 2)First image : Δ A'B'C': A' (2, 21),B'(4, 23), C '(2, 23)Final image Δ A"B"C " :A"(21, 3), B"(1, 1), C "(21, 1)

A 90° clockwise rotation around the origin followed by a translation of 3 units left and 4 units up; congruent


2. Original ABCD: A(22, 1), B(1, 1),C(0, 2), D(22, 2)First image A'B'C 'D': A'(22, 21),B'(1, 21), C '(0, –2), D'(22, 22)Final image A"B"C "D": A"(24, 22),B"(2, 22), C "(0, 24), D"(24, 24)

A reflection across the x-axis followed by a dilation with a scale factor of 2 with the origin as the center of dilation; similar

Lesson Quiz : Part-II


Find a sequence of at least two combined transformations from the original to the final image.

180° rotation around the origin followed by a translation of 1 unitright and 1 unit down.

Lesson Quiz : Part-III


Lesson Quiz for Student Response System

1. Triangle ABC has the following coordinates: A(–5, 1), B(–2, 4), C(–1, 1). Which triangle coordinates represent a reflection across the y-axis?

A. A’(–5, 1), B’(–2, 4), C’(–1, 1)B. A’(5, 1), B’(2, 4), C’(1, 1)C. A’(–5, –1), B’(–2, –4), C’(–1, –1)D. A’(1, –5), B’(4, –2), C’(1, –1)


A. A’(–5, 1), B’(–2, 4), C’(–1, 1)B. A’(5, 1), B’(2, 4), C’(1, 1)C. A’(–5, –1), B’(–2, –4), C’(–1, –1)D. A’(1, 5), B’(4, 2), C’(1, 1)

2. Triangle ABC has the following coordinates: A(–5, 1), B(–2, 4), C(–1, 1). Which triangle coordinates represent a 90 clockwise rotation around the origin?

Lesson Quiz for Student Response System

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