Multiple Transformations

Identify the rule to describe the translation of the triangle ABC to the triangle A′B′C′.

• (x , y ) → (x – 4, y + 3)

• (x , y ) → (x + 3, y + 4)

• (x , y ) → (x + 4, y + 3)

• (x , y ) → (x + 4, y – 3)

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CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

Which statement describes a possible sequence of transformations that transforms figure 1 into figure 2?

• a reflection across the x-axis, followed by a translation 2 units to the left

• a reflection across the x-axis, followed by a translation 3 units to the right

• a rotation 180° clockwise about the origin followed by a translation 2 units to the left

• a rotation 180° clockwise about the origin followed by a translation 3 units to the right

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CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

Figure 3 can also be created by transforming figure 1 with a sequence of two transformations. Which statement describes a possible sequence of transformations that transforms figure 1 into figure 3?

• a rotation 180° clockwise about the origin, followed by translation 2 units to the left

• a rotation 90° clockwise about the origin, followed by a reflection across the x-axis

• a rotation 180° clockwise about the origin, followed by a reflection across the y-axis

• a rotation 90° clockwise about the origin, followed by a translation 3 units to the right

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CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6

Which set of transformations returns a given figure to its original location?

• translation 2 units left, then 3 units up, then 3 units right, then 2 units down

• reflect across the y-axis, then the x-axis, then the y-axis, then the x-axis

• 180° counterclockwise rotation

• 90° clockwise rotation, then reflection across the axis it just rotated over

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CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

Parallelogram A’B’C’D’ (not shown) is the image of parallelogram ABCD after a rotation of 180° about the origin.

Which statements about parallelogram A’B’C’D’ are true?Select each correct statement.

• $Line\ Segments\ AB\ and\ BC\ are\ \parallel$

• $Line\ Segments\ AB\ and\ AD\ are\ \parallel$

• $Line\ Segments\ AB\ and\ CD\ are\ \parallel$

• $Line\ Segments\ AD\ and\ BC\ are\ \parallel$

• $Line\ Segments\ AD\ and\ DC\ are\ \parallel$

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CCSS.HSG.CO.B.6

CCSS.HSG.CO.C.9

CCSS.HSG.GPE.B.5

Parallelogram A’B’C’D’ (not shown) is the image of parallelogram ABCD after a rotation of 90 degrees counterclockwise about the origin.

Which one of the following statements is true?

• Figure A’B’C’D’ will be in Quadrant I, with a vertex on the x-axis.

• Figure A’B’C’D’ will be in Quadrant I, with a vertex on the y-axis.

• Figure A’B’C’D’ will be in Quadrant III, with a vertex on the x-axis.

• Figure A’B’C’D’ will be in Quadrant III, with a vertex on the y-axis.

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CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

Parallelogram A’B’C’D’ (not shown) is the image of parallelogram ABCD after a rotation of 90 degrees counterclockwise about the origin.

Which of the following statements about Figure A’B’C’D’ are true? Circle each correct statement.

• $Line\ Segments\ A'B'\ and\ A'D'\ are\ \parallel$

• $Line\ Segments\ A'B'\ and\ B'C'\ are\ \parallel$

• $Line\ Segments\ B'C'\ and\ A'D'\ are\ \parallel$

• $Line\ Segments\ A'B'\ and\ C'D'\ are\ \parallel$

• $Line\ Segments\ B'C'\ and\ C'D'\ are\ \parallel$

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CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.C.9

CCSS.HSG.GPE.B.5

Triangle PQR is rotated 90° counterclockwise about the origin to form the image triangle P’Q’R’ (not shown). Then triangle P’Q’R’ is reflected across the x-axis to form triangle P’’Q’’R’’ (not shown).

What are the signs of the coordinates (x, y) of point P’?

• Both x and y are positive.

• x is negative and y is positive.

• Both x and y are negative.

• x is positive and y is negative.

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CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

Triangle PQR is rotated 90° counterclockwise about the origin to form the image triangle P’Q’R’ (not shown). Then triangle P’Q’R’ is reflected across the x-axis to form triangle P’’Q’’R’’ (not shown).

What are the signs of the coordinates (x, y) of point Q′′?

• Both x and y are positive.

• x is negative and y is positive.

• Both x and y are negative.

• x is positive and y is negative.

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CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

Lines m and n are parallel on a coordinate plane. Lines m and n are transformed by the samerotation‚ resulting in image lines s and t. Which statement describes the relationship between lines sand t?

• Lines s and t are parallel.

• Lines s and t are perpendicular.

• Lines s and t are intersecting but not perpendicular.

• The relationship between lines s and t cannot be determined without knowing the angle of therotation.

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CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6