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

Neither of the choices is correct.

Explanation:

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

(10, - 5)(15, -5)(10, - 10)(15, -10)

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

(0,10)(0,15)(-5,10)(-5, 15)

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:

(10, - 5) → (-5, -10)(15, -5) → (-5, -15)(10, - 10) → (-10, -10)(15, -10) → (-10, -15)

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:

(x, y) → (-x, -y) → (-x + 10, -y)

That means:

(10, - 5) → (-10,5) → (-10 + 10, 5) = (0, 5)(15, -5) → (-15, 5) → (-15 + 10, 5) = (-5, 5)(10, - 10) → (-10, 10) → (-10 + 10, 10) = (0, 10)(15, -10) → (-15, 10) → (-15 + 10, 10) = (-5, 10)

        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.

The answer would be a i think

It is going to be the third choice