Test #1 Rigid Motions

Which of the following are the vertices of the image of the figure below under the translation (x, (x,y)→(x+1,y−3)?

• (1, -3) , (-1, 3), (3, 1)

• (-7, 7) , (1, 4), (-4, 1)

• (-5, 1) , (3, -2), (-2, -5)

• (-9, 5) , (-1, 2), (-6, -1)

Tags

CCSS.8.G.A.1

CCSS.8.G.A.3

Which of the following statements are true? Select all that apply.

• The image of the point (−3,−5) under a reflection across the x-axis is (3,−5).

• The image of the point (1,9) under a reflection across the y-axis is (1,−9).

• The image of the point (8,7) under a reflection across the line y=−x is (−7,−8).

• The image of the point (−6,−6) under a reflection across the line y=x is (−6,−6).

• The image of the point (2,4) under a reflection across the y-axis followed by a reflection across y=x is (−2,−4).

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

Quadrilateral KMBG is shown on the coordinate grid.Apply the sequence of transformations on quadrilateral KMBG to form quadrilateral HTDZ.
∙(x,y)→(y,−x)
∙(x,y)→(x+2,y+3)
What is the resulting image?

• 
• 
• 
• 

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

Triangle RZX is shown on the coordinate grid.Apply the sequence of transformations on △RZX to form △HGK.
∙(x,y)→(−x,y)
∙(x,y)→(x−3,y+4)
What is the resulting image?

• 
• 
• 
• 

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

Identify all sequences of transformations where the image is congruent to the pre-image.

• Rotate about the origin clockwise 90∘, then dilate by a scale factor of 56.

• Reflect across the x-axis, then translate left 1 unit and up 11 units.

• Dilate by a scale factor of 14, then reflect across the y-axis.

• Rotate about the origin counterclockwise 90∘, then reflect across the line y=3.

• Translate the pre-image right 4 units and down 3 units. Then, rotate about the origin counterclockwise 180∘.

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

If you wanted to reflect a line segment with one endpoint at (x,y) about the x-axis, which of the following describes how you might go about finding the coordinates for the new point after the reflection?

• (x, -y)

• (-x, y)

• (y, x)

• (-y, -x)

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

Triangles YTW, Y′T′W′, and Y″T″W″ are shown on the coordinate grid. Which of the following multiple transformations was applied?

• Reflection across y-axis followed by rotation 90 degrees counterclockwise.

• Reflection across x-axis followed by rotation 90 degrees counterclockwise.

• Reflection across y-axis followed by rotation 180 degrees counterclockwise.

• Reflection across y-axis followed by rotation 90 degrees clockwise.

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

Triangle  BMR and its transformations are shown on the coordinate grid. What figure is the result of a reflection over the x-axis of triangle BMR ?

• Figure P

• Figure T

• Figure I

• Figure F

Tags

CCSS.8.G.A.1

CCSS.8.G.A.3

Point A(−7,−2) is rotated 270∘ counterclockwise and then shifted down 3 units.
What are the coordinates of A"?

• (2, 4)

• (-2, -7)

• (-2, 4)

• (7, -5)

Tags

CCSS.8.G.A.1

CCSS.8.G.A.3

Triangle A′B′C′with coordinates of A′(−6,2),B′(−4,2), and C′(−6,−2) is the image of triangle ABC after a translation of (x−3,y+2). What could be possible coordinates for the original vertices of triangle ABC? Select all that apply.

• (-3, 0)

• (-1, 0)

• (-9, 4)

• (-7, 4)

• (-3, -4)

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3