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29.07.2022

Rotate the figure 90 degrees clockwise then translate 4 units left

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09.07.2023, solved by verified expert

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If I am not mistaken, the new figure will be here (view attachment, bright blue figure is the new transformation)

Rotate the figure 90 degrees clockwise then translate, №18011253, 29.07.2022 11:58

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Mathematics

Rotate the figure 90 degrees clockwise then translate 4 units left

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P Answered by Master

If I am not mistaken, the new figure will be here (view attachment, bright blue figure is the new transformation)

Rotate the figure 90 degrees clockwise then translate 4 units left

Mathematics

What are two possible transformations that together could have been used to create the red figure from the blue figure? a) a reflection across the x axis followed by a reflection across the y axis b) a translation of 1 unit down followed by a rotation of 90 degrees clockwise about the origin c) a rotation of 90 degrees counterclockwise about the origin followed by a reflection across the x axis d) a rotation of 90 degrees counterclockwise about the origin followed by a translation of 1 unit down

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P Answered by Specialist

4

I think its either C or D give me one second to figure it out.

Mathematics

What are two possible transformations that together could have been used to create the red figure from the blue figure? a) a reflection across the x axis followed by a reflection across the y axis b) a translation of 1 unit down followed by a rotation of 90 degrees clockwise about the origin c) a rotation of 90 degrees counterclockwise about the origin followed by a reflection across the x axis d) a rotation of 90 degrees counterclockwise about the origin followed by a translation of 1 unit down

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P Answered by Master

4

I think its either C or D give me one second to figure it out.

Mathematics

Which sequence of transformations produces an image that is not congruent to the original figure? a. a translation of 4 units to the right followed by a dilation of 2. b. a rotation of 90 degrees clockwise followed by a translation of 2 units to the left. c. a translation of 3 units to the left followed by a reflection across the y-axis. d. a reflection across the y-axis followed by a rotation of 90 degrees counterclockwise.

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P Answered by PhD

117

The correct answer is:

A) A translation of 4 units to the right followed by a dilation of 2.

Explanation:

3 of our transformations are called isometries. These are transformations that preserve the size and shape of the original figure; they just change the position or orientation of it. Translations, reflections and rotations are all isometries. We know that isometries preserve congruence, since they maintain the size and shape of the original figure.

A dilation is not an isometry. This is because a dilation changes the size of a figure. Since the new figure will not be the same size as the original, they will not be congruent.

Mathematics

Which sequence of transformations produces an image that is not congruent to the original figure? a. a translation of 4 units to the right followed by a dilation of 2. b. a rotation of 90 degrees clockwise followed by a translation of 2 units to the left. c. a translation of 3 units to the left followed by a reflection across the y-axis. d. a reflection across the y-axis followed by a rotation of 90 degrees counterclockwise.

Step-by-step answer

P Answered by PhD

117

The correct answer is:

A) A translation of 4 units to the right followed by a dilation of 2.

Explanation:

3 of our transformations are called isometries. These are transformations that preserve the size and shape of the original figure; they just change the position or orientation of it. Translations, reflections and rotations are all isometries. We know that isometries preserve congruence, since they maintain the size and shape of the original figure.

A dilation is not an isometry. This is because a dilation changes the size of a figure. Since the new figure will not be the same size as the original, they will not be congruent.

Mathematics

Which transformations will produce similar, but not congruent figures? a.) triangle mno is reflected across the x-axis and then rotated 90 degrees clockwise to form triangle m n o . b.) triangle mno is reflected across the x-axis and then translated 9 units down to form triangle m n o . c.) triangle mno is reflected across the y-axis and then dilated by a scale factor of 1.8 to form triangle m n o . d.) triangle mno is reflected across the y-axis and then rotated 180 degrees clockwise to form triangle m n o .

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P Answered by PhD

79

If you rotate, translate, or reflect a figure, the afterimage will be congruent to the original.
But if you dilate the figure, you are changing the dimensions and the length of its sides. However, angle measures are preserved and therefore that makes the figure and its afterimage similar.
Therefore C.) produces a similar but not congruent figure because there is the dilation in it.

Mathematics

Which transformations will produce similar, but not congruent figures? a.) triangle mno is reflected across the x-axis and then rotated 90 degrees clockwise to form triangle m n o . b.) triangle mno is reflected across the x-axis and then translated 9 units down to form triangle m n o . c.) triangle mno is reflected across the y-axis and then dilated by a scale factor of 1.8 to form triangle m n o . d.) triangle mno is reflected across the y-axis and then rotated 180 degrees clockwise to form triangle m n o .

Step-by-step answer

P Answered by PhD

79

If you rotate, translate, or reflect a figure, the afterimage will be congruent to the original.
But if you dilate the figure, you are changing the dimensions and the length of its sides. However, angle measures are preserved and therefore that makes the figure and its afterimage similar.
Therefore C.) produces a similar but not congruent figure because there is the dilation in it.

Mathematics

A parallelogram with coordinates A (-2,3), B (3,3), C (4,6), and D(-1,6) is the first rotated 90 degrees clockwise and then translated 4 units left and 2 units down to form quadrilateral A B C D what is the distance, in units between point C and point D in the resulting figure

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P Answered by PhD

14

Given:

The vertices of a parallelogram are A (-2,3), B (3,3), C (4,6), and D(-1,6).

It is first rotated 90 degrees clockwise and then translated 4 units left and 2 units down to form quadrilateral A'B'C'D.

To find:

The distance between C' and D'.

Solution:

If a figure rotated 90 degrees clockwise, then

$(x,y)\to (y,-x)$

$C(4,6)\to C_1(6,-4)$

$D(-1,6)\to D_1(6,-(-1))=D_1(6,1)$

If figure translated 4 units left and 2 units down, then

$(x,y)\to (x-4,y-2)$

$C_1(6,-4)\to C'(6-4,-4-2)=C'(2,-6)$

$D_1(6,1)\to D'(6-4,1-2)=D'(2,-1)$

Distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Distance between C'(2,-6) and D'(2,-1) is

$C'D'=\sqrt{(2-2)^2+(-1-(-6))^2}$

$C'D'=\sqrt{(0)^2+(-1+6)^2}$

$C'D'=\sqrt{(5)^2}$

C'D'=5

Therefore, the distance between C'D' is 5 units.

Mathematics

Carmen performed two transformations on the blue figure. what transformations did she perform to get the red figure? a) a reflection across the y axis followed by a reflection across the x axis b) a translation of 5 units right and 1 unit down followed by a reflection across the x axis c) a reflection across the x axis followed by a reflection across the y axis d) a translation of 5 units right and 1 unit down followed by a rotation of 90 degrees clockwise about the origin

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P Answered by PhD

6

B) a translation of 5 units right and 1 unit down followed by a reflection across the x axis

Mathematics

Carmen performed two transformations on the blue figure. what transformations did she perform to get the red figure? a) a reflection across the y axis followed by a reflection across the x axis b) a translation of 5 units right and 1 unit down followed by a reflection across the x axis c) a reflection across the x axis followed by a reflection across the y axis d) a translation of 5 units right and 1 unit down followed by a rotation of 90 degrees clockwise about the origin

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P Answered by PhD

6

B) a translation of 5 units right and 1 unit down followed by a reflection across the x axis

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