Which series of transformations shows that pentagon A is congruent to pentagon B?

A.
Reflect pentagon A over the y-axis, rotate it 180° clockwise about the origin, and translate it 3 units up.

B.
Rotate pentagon A 90° clockwise about the point (1, 1), reflect it over the x-axis, and translate it 3 units to the left.

C.
Rotate pentagon A 90° clockwise about the origin, reflect it over the x-axis, and translate it 6 units to the left.

D.
Reflect pentagon A over the y-axis and translate it 2 units to the left and 8 units up.

Question

02-09-2022
Mathematics

contestada

Which series of transformations shows that pentagon A is congruent to pentagon B?

A.
Reflect pentagon A over the y-axis, rotate it 180° clockwise about the origin, and translate it 3 units up.

B.
Rotate pentagon A 90° clockwise about the point (1, 1), reflect it over the x-axis, and translate it 3 units to the left.

C.
Rotate pentagon A 90° clockwise about the origin, reflect it over the x-axis, and translate it 6 units to the left.

D.
Reflect pentagon A over the y-axis and translate it 2 units to the left and 8 units up.

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joaobezerra joaobezerra · Answer 1 · 2022-09-07T19:15:31+02:00

Using translation concepts, the series of transformations that shows that pentagon A is congruent to pentagon B is:

B. Rotate pentagon A 90° clockwise about the point (1, 1), reflect it over the x-axis, and translate it 3 units to the left.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, we have that the Pentagons have different orientations, meaning that it was rotated, eliminating options A and D.

For the vertices to reach the position they reached in Pentagon B, there had to be a shift left, and before the shift left, the Pentagon must have been entirely at the fourth quadrant, meaning that it was reflected about the point (1,1), and option B is correct.

More can be learned about translation concepts at https://brainly.com/question/4521517

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