Which sequence of transformations confirms congruence by mapping shape i onto shape ii?

a reflection across the x axis and 15 units left

a 90 degree clockwise rotation about the origin and the 25 units up

a 90 degree counterclockwise rotation about the origin then a translation 10 units up

a 180 degree rotation about the origin and the a translation 10 units right

Explanation:

1. Coordinates of the vertices of the figure I (preimage):

2. Coordinates of the vertices of the figure II (image):

Since many different rigid transformations can map the figure I into the figue II, you will need to use trial and error.

The most important is to do it in an educated way.

I will start by eliminating some options.

The first option, a reflection across the x-axis and 15 units left, does not work, because the reflection across the x-axis would shift the figure to a lower position than what you need.

The third option, a 90º counterclokwise rotation about the origin then a translation 10 units up, would move the figure to the second quadrant, and we need it in the third quadrant.

I will try now with the second choice, a 90º clockwise rotation and then 25 units up:

First, a 90º clockwise rotation, which is the same that a 270º counterclockwise rotation, follows the rule (x, y) → (y, -x)

Then, that results in:

Now, you can see that shifting 25 units up will not work, because you need that two x-coordinates become 0 (zero). So, this is not the correct set of transformations either.

A 180º rotation about the origin and a translation 10 units right follow this chain of rules:

That means:

        These last points do not coincide either with the vertices of the figure II.

In conclusion, neither of the choices gives the correct answer to the question.

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step-by-step explanation:

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