Question

If triangle ABC is reflected over the x‐axis, reflected over the y‐axis, and rotated 180 degrees, where will point B' lie?

(−1, 4)
(1, −4)
(4, −1)
(−4, 1)

Answer 1

A reflection over the x-axis changes the sign on the y-coordinate. A reflection over the y-axis changes the sign on the x-coordinate. Rotating by 180 degrees reverses the x- and y-coordinates.

Answer 2

@ospreytriple i doth get it

Answer 3

Looking at the given diagram, what are the coordinates of point B?

Answer 4

-1,4

Answer 5

Great. So first apply a reflection over the x-axis. As I said earlier, the sign on the y-coordinate changes. What are the new coordinates?

Answer 6

how do i do that

Answer 7

i am really bad at geometry

Answer 8

Change the sign on the y-coordinate. It it's positive, it becomes negative. If it's negative, it becomes positive.

Answer 9

so -1,-4

Answer 10

correct?

Answer 11

so choice a

Answer 12

Good. Now apply the reflection over the y-axis. In this transformation, the sign on the x-coordinate changes. What does that give you?

Answer 13

1,-4

Answer 14

so choice b?

Answer 15

Good. Now finally, rotate by 180 degrees. In this transformation, both coordinate change sign (I messed up when I tried to explain above). What does this give you?

Answer 16

-1,4?

Answer 17

Correct. Good job!

Answer 18

you sure?

Answer 19

Yup. Draw it out for yourself to confirm.

Answer 20

it will be on the same position as B

Answer 21

That's right. It ends up right back where it started.

Answer 22

Wouldn't that be 360?

Answer 23

You have performed three transformations, reflection across x-axis, reflection across y-axis, and rotation of 180 degrees. Not just a 180-degree rotation.

Answer 24

so what would 360 and 180 rotation for point b

Answer 25

I don't understand your question? Please explain.

Answer 26

i confused what my answer would be

Answer 27

Why? You have your answer.

Answer 28

ohh k

Answer 29

it just looks weird to me

Answer 30

Well then, draw it out. That's what you should be doing anyway.