Which sequence of transformations confirms congruence by mapping shape I onto shape II?

Mathematics

2 answers:

Lubov Fominskaja [6]3 years ago

8 0

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: