Question

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°

Answer 1

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°

Answer 2

The set of reflections and rotations that carry rectangle ABCD onto itself are: rotate $180^\circ$, 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 $180^\circ$. Therefore, this option is incorrect.

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

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

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

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