Question

Polygons ABCD and A′B′C′D′ are shown on the coordinate grid:

A coordinate plane is shown with two polygons represented. Polygon ABCD has vertices A at 2 comma 2, B at 2 comma 4, C at 3 comma 5 and D at 3 comma 1. Polygon A prime B prime C prime D prime has vertices A at negative 1 comma negative 2, B at negative 1 comma negative 4, C at negative 2 comma negative 5, and D at negative 2 comma negative 1.
What set of transformations is performed on ABCD to form A′B′C′D′?

a
A translation 1 unit to the left followed by a 180-degree counterclockwise rotation about the origin

b
A translation 1 unit to the right followed by a 180-degree counterclockwise rotation about the origin

c
A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the right

d
A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left

Answer 1

To make it easier to read, Idk if this was done on purpose. But let me organize your question.

A = (2,2)
B = (2,4)
C = (3,5)
D = (3,1)

And a polygon is the subject being transformed. So if it was translated 1 unit to the left, then all your coordinates are given to go back by one.

That would mean A = (1,1), B = (1,3), C = (2,4), and D = (2,0). And then given a 180 turn. So you know that TikTok song where it's like, "Did a full one-eightyyyy, crazyyy..." Right? The way the tiktokers are spinning is actually 360, so 180 is half of that. Instead of doing a full turn, it's more like you're walking towards somewhere and then you just turn around completely to face the opposite direction you were facing prior.

Answer 2

For Option B, it says 1 unit to the right and 180 degrees turn counterclockwise. So basically the same thing that I applied in my previous post, but instead of left, it's right. So the given is isolated and all you have to do is translate it the right once. Only x is translated because it's horizontal, it can go right or left. Y is translated up and down.

Answer 3

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Razor
And a polygon is the subject being transformed. So if it was translated 1 unit to the left, then all your coordinates are given to go back by one.

That would mean A = (1,1), B = (1,3), C = (2,4), and D = (2,0).
\(\color{#0cbb34}{\text{End of Quote}}\)
I made a mistake here, ignore it. A = (1,2), B = (1,4), C = (2,5), and D = (2,1).

Answer 4

I should have given you enough information to figure this out by yourself. I'm sorry no one responded to this earlier, people here come here for help in Math, so not a lot of people are good at it.