Answer:
- 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.
