Multiple Transformations

Sequencing Transformations

Multiple Choice

Point (4,5) is rotated 180. What are the new coordinates?

• (-4,-5)

• (-5,4)

• (4,-5)

Multiple Choice

Point (2,5) is reflected across the y-axis. What is the new coordinate?

• (-2,5)

• (5,2)

• (2,-5)

Multiple Choice

Point (10,3) is reflected across the x-axis. What is the new coordinate?

• (3,10)

• (-10,3)

• (10,-3)

Multiple Choice

Point (4,5) is rotated 90 clockwise. What are the new coordinates?

• (-4,-5)

• (-5,4)

• (4,-5)

Multiple Transformations

• Sometimes more than one transformation is applied to an image. When this happens, you will do one transformation and then a second one. Let's look at some examples.

Example: Translate, Then Reflect

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Rectangle LMNO was translated 4 units down and 2 units right (x+2, y-4).

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Then, the new image was reflected over the y-axis. Sketch the image after the translation and reflection.

After the translation, the new points for rectangle LMNO  are L'(-4,-1), M'(-4,-3), N'(1,-3), and O'(1,-1). Once we have translated, we can now reflected those new points over the y-axis.

So, after a translation of down 4 units 2 units right and then a reflection over the y-axis, the new coordinates of rectangle LMNO are 

L'(4, -1), M'(4, -3), N'(-1, -3), and O'(-1, -1).

Multiple Choice

What are the series of rigid motions that would map ∆ABC onto ∆A''B''C''?

• a reflection followed by a rotation
• a reflection followed by a translation
• a translation followed by a rotation
• a translation followed by a reflection

Multiple Choice

Two triangles are shown on the coordinate grid. Which sequence of transformations shows that

$$\Delta ABC\cong\Delta DEF$$  

• Reflect △ABC across the x-axis, then translate it down 1

• Reflect △ABC across the x-axis, then translate it up 1

• Reflect △ABC across the y-axis, then translate it down 1

• Reflect △ABC across the y-axis, then translate it up 1

Multiple Choice

Two triangles are shown on the coordinate grid. Which sequence of transformations shows that ΔABC≅ΔDEF

• Reflect △ABC across the x-axis, then translate it right 1

• Reflect △ABC across the y-axis, then translate it right 1

• Reflect △ABC across the x-axis, then translate it left 1

• Reflect △ABC across the y-axis, then translate it left 1

Multiple Choice

Plot A(4,1) B(5,4) C(1,2). Reflect it over the x-axis, then translate it 3 units left. What are the coordinates of A'B'C'?

• A' (-1, -1) B' (-2, -4) C' (2, -2)

• A' (4, -4) B' (5, -7) C' (1, -5)

• A' (-7, 1) B' (-8, 4) C' (-4, 2)

• A' (1, -1) B' (2, -4) C' (-2, -2)

Multiple Choice

The design started with the small red heart. Which transformation was used to create the larger hearts in the design?

• Dilation
• Reflection
• Rotation
• Translation

Multiple Choice

What type of transformation does this demonstrate?

• Translation

• Rotation

• Reflection

Multiple Choice

The hour hand on a clock moves from 9:00 to 11:00. What type of transformation does this demonstrate?

• Dilation
• Reflection
• Rotation
• Translation

Multiple Choice

Quadrilateral QRST is rotated 180° about the origin, resulting in quadrilateral Q'R'S'T' as seen in the figure.

Which series of transformations would have the same result as the above transformation

• A reflection across the x-axis and then a reflection across the y-axis

• A translation 8 units to the left and then a reflection across the y-axis

• a 90° clockwise rotation about the origin and then a reflection across the x-axis

• A translation 8 units to the right and then a 90° clockwise rotation about the origin.

Multiple Choice

Plot A(1,1) B(3,1) C(2,4). Rotate it 90° clockwise, then reflect it over the y-axis. What are the new coordinates of A'B'C'?

• A' (-1, -1) B' (-1, -3) C' (-4, -2)

• A' (-1, 1) B' (-1, 3) C' (-4, 2)

• A' (1, -1) B' (1, -3) C' (4, -2)

• A' (-1, -1) B' (-3, -1) C' (-2, -4 )

Multiple Choice

Plot A(4,1) B(5,4) C(1,2). Reflect it over the x-axis, then translate it 3 units left. What are the coordinates of A'B'C'?

• A' (-1, -1) B' (-2, -4) C' (2, -2)

• A' (4, -4) B' (5, -7) C' (1, -5)

• A' (-7, 1) B' (-8, 4) C' (-4, 2)

• A' (1, -1) B' (2, -4) C' (-2, -2)

Multiple Choice

Two triangles are shown on the coordinate grid. Which sequence of transformation shows that  $$\Delta ABC\cong\Delta DEF$$  ?

• Reflect △ABC across the x-axis, then translate it down 2

• Reflect △ABC across the y-axis, then translate it down 2

• Reflect △ABC across the x-axis, then translate it up 2

• Reflect △ABC across the y-axis, then translate it up 2