Rectangle ABCD is reflected over the x-axis, followed by a reflection over the y-axis, and then rotated 180 degrees about the origin. What is the location of point A after the transformations are complete?

Select one:
a. (−5, 1)
b. (5, −1)
c. (−5, −1)
d. (5, 1)

Question

Rectangle ABCD is reflected over the x-axis, followed by a reflection over the y-axis, and then rotated 180 degrees about the origin. What is the location of point A after the transformations are complete? 

Select one:
a. (−5, 1)
b. (5, −1)
c. (−5, −1)
d. (5, 1)

simplymarie_x · Answer

attachment

anthonyym · Answer

One step at a time. 
What do you get when you reflect A over x-axis?

simplymarie_x · Answer

So it's (x, y) -> (x, -y)

(-5, 1) -> (-5, -1) ?

Right?

anthonyym · Answer

Yes you get (-5, -1).

anthonyym · Answer

Now reflect (-5, -1) over y-axis. The sign of the x-coordinate will be flipped.

anthonyym · Answer

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anthonyym · Answer

Then you have to rotate 180 degrees about the origin.

simplymarie_x · Answer

Isn't that just (-5, -1) -> (-x, -y)
(-5, -1) -> (5, 1)

anthonyym · Answer

Yes that's correct.

simplymarie_x · Answer

Okay, thanks. :-)

anthonyym · Answer

no problem

boldjon · Answer

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anthonyym · Answer

Hey sorry we should have rotated the point (5, -1) about origin.

simplymarie_x · Answer

Huh?

anthonyym · Answer

We started with point (-5, 1)
Reflect over x-axis: (-5, -1)
Reflect over y-axis: (5, -1)
Then rotate that point (5, -1) degrees about origin

anthonyym · Answer

*180 degrees

simplymarie_x · Answer

Okay, so then it's (5, -1) -> (-x, -y)

(-5, 1)

anthonyym · Answer

Yes that's correct.
|dw:1460925826151:dw|