Identifying Combined Transformations5-8
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Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
Identifying Combined Transformations5-8
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.
Identifying Combined Transformations5-8
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
Identifying Combined Transformations5-8
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.
Identifying Combined Transformations5-8
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
Identifying Combined Transformations5-8
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
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 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.
Identifying Combined Transformations5-8
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)
Identifying Combined Transformations5-8
Lesson Quizzes
Lesson Quiz for Student Response Systems
Standard Lesson Quiz
Identifying Combined Transformations5-8
Lesson Quiz : Part-I
Identify the combined transformations from the original to the final image, and tell whether the two figures are similar or congruent.
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
Identifying Combined Transformations5-8
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
Identifying Combined Transformations5-8
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
Identifying Combined Transformations5-8
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)
Identifying Combined Transformations5-8
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