Question

Use the graph to answer the question.

2016 StrongMind. Created using GeoGebra
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O a rotation 90° clockwise about the origin, followed by a translation 3 units down
O a reflection in the y-axis, followed by a rotation 90° clockwise about the origin
O a translation 3 units down, followed by a rotation 90 clockwise about the origin
O a reflection in the z-axis, followed by a reflection in the g-axis
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Long Description Image of Parallelograms
Which series of transformations shows that parallelogram ABCD is congruent to parallelogram A'B'C'D' by superimposing one onto the other?

Answer 1

The correct answer is a reflection in the y-axis, followed by a rotation 90° clockwise about the origin. Option B is the right choice.

To see this, let's imagine that we can superimpose parallelogram ABCD onto parallelogram A'B'C'D'.

In order to do this, we need to perform a transformation that will move ABCD to the same position as A'B'C'D'.

If we reflect ABCD in the y-axis, we will get parallelogram A'B'C'D'. However, A'B'C'D' is rotated 90° clockwise relative to ABCD. To fix this, we can rotate ABCD 90° clockwise about the origin.

The following image shows the two parallelograms superimposed after the reflection in the y-axis and the rotation 90° clockwise about the origin:

Therefore, the series of transformations that shows that parallelogram ABCD is congruent to parallelogram A'B'C'D' by superimposing one onto the other is a reflection in the y-axis, followed by a rotation 90° clockwise about the origin.

Option B is the right choice.