Multiple Transformations

Presentation

•

Mathematics

•

8th Grade

•

Hard

Joseph Anderson

FREE Resource

5 Slides • 15 Questions

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

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

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

Sequencing Transformations

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