What set of reflections would carry hexagon ABCDEF onto itself? Hexagon ABCDEF on the coordinate plane with point A at negative 1, 1, point B at negative 3, 1, point C at negative 4, 2, point D at negative 3, 3, point E at negative 1, 3, and point F at 0, 2. x-axis, y=x, x-axis, y=x y=x, x-axis, y=x, y-axis y-axis, x-axis, y-axis x-axis, y-axis, y-axis

- anonymous

- katieb

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- anonymous

- anonymous

A ) x-axis, y=x, x-axis, y=x
B ) y=x, x-axis, y=x, y-axis
C ) y-axis, x-axis, y-axis
D ) x-axis, y-axis, y-axis

- anonymous

I think its B, am I right?

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## More answers

- anonymous

@Nnesha @campbell_st @phi @ParthKohli
would any of you please help me? i need an understanding for this aswell..please :(

- phi

Yes , B sounds good.
It is definitely not C or D
Do you know how to do the various reflections?

- anonymous

why is it B? (im glad i guessed right lol but...its good to know)
no, i do not :(

- anonymous

- anonymous

A reflection is a type of transformation that creates a mirror image of the pre-image across a line of reflection. You learned how images are created across four different lines of reflection:
Across the x-axis
(x, y) → (x, −y)
Across the y-axis
(x, y) → (−x, y)
Across the line y = x
(x, y) → (y, x)
Across a horizontal or vertical line
Count the distance between each point on the figure and the line of reflection. Then, for each point, count this same distance from the line of reflection to find the corresponding point.

- anonymous

is it theses? i got this from the lesson

- anonymous

*these

- phi

yes

- phi

To test a choice, I would pick one point on the figure, and do each of the transforms and see where the point lands after all of the transforms.

- anonymous

how would i test A= (-1,1) ?

- phi

Let's test
B ) y=x, x-axis, y=x, y-axis
using point B (-3,1)
Across the line y = x (x, y) → (y, x)
so we get (1,-3)
Across the x-axis (x, y) → (x, −y)
we get (1,3)
Across the line y = x (x, y) → (y, x)
we get (3,1)
Across the y-axis (x, y) → (−x, y)
we get (-3,1)
that is back where we started. If we do that with all the points, we find the same thing.
all of that hopping around landed us back in the original spot.

- phi

can you try point A using choice B B ) y=x, x-axis, y=x, y-axis ?

- anonymous

so it keep reflecting...technically otating us back to where we started?

- anonymous

rorating*

- anonymous

want me to try point A? or answer A? lol

- phi

point A (-1,1)
using the same transformations I used for point B

- anonymous

ok

- anonymous

sorry it took lon i wrote i out, im going to type it now

- anonymous

long*

- anonymous

Point A (-1,1)
across the line y=x(x,y) -> (y,x)
(1,-1)
across the x-axis (x,y) -> (x,-y)
(1,1)
across the line y=x(x,y) -> (y,x)
(1,1)
across the y-axis (x,y) -> (-x,y)
(-1,1)
did I do this correctly? (it did bring me back to where I start but i wanted to make sure lol) also, these type of reflections are basically formulas, correct? just like shifting in translations?

- phi

yes, looks good.
if you plot the points, the flips across the x-axis or y-axis will be clear.
the only one that is hard to visualize is the flip across y=x (a diagonal line)

- anonymous

also, did we read the question right? it says "carry hexagon ABCDEF onto itself" does onto itself mean back to where it started? (i just wanna make sure)

- anonymous

ohh yay!~ so if I plant the points it will show me it diagnaly reflected? or it wouldnt?

- phi

that means every point gets mapped back onto the hexagon.
It might mean the hexagon comes back flipped around (for example F to C and vice versa)
But in this case each point is mapped back onto itself (we checked 2 points, it is safe to assume it works for the other points)

- phi

***so if I plot the points***
not sure which points you mean.

- anonymous

ok~
and i mean, like if i plot points ABCDEF with the set of reflections of B , would it show me the diagnal reflection? or no?

- phi

if you plot the final result of the reflections in choice B,
each point will be where it started. In other words, the "new" hexagon will lie directly on top of the "old" hexagon. The hexagon was "carried onto itself"

- anonymous

OHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

- anonymous

LOL right! right! ive been out in the sun for too long this morning XD thank you so so so much! i seriously appreciate your help! i jut couldnt get anywhere by just reading the video and some of the terms in the lesson confuse me, but you helped me alot, you were very clear and simple in instructing me! thank you so very very much!~ :)

- phi

yw

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