What set of reflections and rotations would carry rectangle ABCD onto itself? Parallelogram formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at 0, 2, D at negative 1, 1. Rotate 180°, reflect over the x-axis, reflect over the line y=x Reflect over the x-axis, rotate 180°, reflect over the x-axis Rotate 180°, reflect over the y-axis, reflect over the line y=x Reflect over the y-axis, reflect over the x-axis, rotate 180°

Question

04-09-2017
Mathematics

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What set of reflections and rotations would carry rectangle ABCD onto itself? Parallelogram formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at 0, 2, D at negative 1, 1. Rotate 180°, reflect over the x-axis, reflect over the line y=x Reflect over the x-axis, rotate 180°, reflect over the x-axis Rotate 180°, reflect over the y-axis, reflect over the line y=x Reflect over the y-axis, reflect over the x-axis, rotate 180°

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eco92 eco92 · Answer 1 · 2017-09-05T00:07:35+02:00

Each of the 4 choices has been drawn step by step as follows:

the first transformation is drawn in light grey
the second transformation is drawn in dark grey
the third transformation is described as how it should be.

Choice I, picture I:
Rotate 180°, reflect over the x-axis, reflect over the line y=x

the last transformation should be : reflect with respect to the y-axis

Choice II, picture II:
Reflect over the x-axis, rotate 180°, reflect over the x-axis

the last transformation should be : reflect with respect to the y-axis

Choice III, picture III:
Rotate 180°, reflect over the y-axis, reflect over the line y=x

the last transformation should be : reflect with respect to the x-axis

Choice IV, picture IV:
Reflect over the y-axis, reflect over the x-axis, rotate 180°

the last transformation should be : rotate 180° CORRECT!

Answer: Reflect over the y-axis, reflect over the x-axis, rotate 180°

ahirohit963 ahirohit963 · Answer 2 · 2021-11-11T08:58:49+01:00

The set of reflections and rotations that carry rectangle ABCD onto itself are: rotate [tex]180^\circ[/tex], reflect over the y-axis, reflect over the line y = x.

For solving this question we have to go through the options and their respective graphs.

Option A) - Reflect over the y-axis, reflect over the x-axis, rotate [tex]180^\circ[/tex]. Therefore, this option is incorrect.

Option B) - Rotate [tex]180^\circ[/tex], reflect over the x-axis, reflect over the line y = x. Therefore, this option is incorrect.

Option C) - Reflect over the x-axis, rotate [tex]180^\circ[/tex], reflect over the x-axis. Therefore, this option is incorrect.

Option D) - Rotate [tex]180^\circ[/tex], reflect over the y-axis, reflect over the line y = x. Therefore, this option is correct.

For more information, refer to the link given below:

https://brainly.com/question/16608196