What Set of Reflections Would Carry Hexagon Abcdef Onto Itself

Mathematics

OpenStudy (anonymous):

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

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OpenStudy (anonymous):

OpenStudy (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

OpenStudy (anonymous):

I think its B, am I right?

OpenStudy (anonymous):

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

OpenStudy (phi):

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

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OpenStudy (anonymous):

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

OpenStudy (anonymous):

@phi

OpenStudy (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.

OpenStudy (anonymous):

is it theses? i got this from the lesson

OpenStudy (anonymous):

*these

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OpenStudy (phi):

yes

OpenStudy (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.

OpenStudy (anonymous):

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

OpenStudy (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.

OpenStudy (phi):

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

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OpenStudy (anonymous):

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

OpenStudy (anonymous):

rorating*

OpenStudy (anonymous):

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

OpenStudy (phi):

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

OpenStudy (anonymous):

ok

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OpenStudy (anonymous):

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

OpenStudy (anonymous):

long*

OpenStudy (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?

OpenStudy (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)

OpenStudy (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)

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OpenStudy (anonymous):

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

OpenStudy (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)

OpenStudy (phi):

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

OpenStudy (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?

OpenStudy (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”

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OpenStudy (anonymous):

OHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

OpenStudy (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!~ 🙂

OpenStudy (phi):

yw

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### What Set of Reflections Would Carry Hexagon Abcdef Onto Itself

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