Question

What set of transformations could be applied to rectangle ABCD to create A'B'C'D'?

reflected over the x-axis and rotated 180�

reflected over the y-axis and rotated 180�

reflected over the x-axis and rotated 90� counterclockwise

reflected over the y-axis and rotated 90� counterclockwise

Answer 1

Can you please help with this one @ganeshie8 the 1/2 are suppose to be degrees

Answer 2

we use below :-

180 degree rotation : (x, y) -> (-x, -y)
90 degree rotation counterclockwise : (x, y) -> (-y, x)
90 degree rotation clockwise : (x, y) -> (y, -x)

Answer 3

save them for later,
actually this problem is much easier than it looks :)

Answer 4

lets take one point, say "D", and see how it goes wid each of the given options

Answer 5

to start wid,
D is in 2nd quadrant right ?

Answer 6

Ok

Answer 7

lets see wat happens to it after first option :-
reflected over the x-axis and rotated 180�

Answer 8

reflection in x-axis :
takes "D" from 2nd quadrant to 3rd quadrant

rotating 180 degrees :
takes it to 1st quadrant

Answer 9

but D' is in 3rd quadrant. so optionA is WRONG.

Answer 10

lets try second option similarly

Answer 11

reflected over the y-axis and rotated 180�

reflection over y-axis :
takes "D" from 2nd quadrant to 1st quadrant


rotating 180 degree :
takes it to 3rd quadrant

Answer 12

but D' is in 4th quadrant, so optionB is also wrong

Answer 13

similarly can u try and see if optionC is corrrect ?

Answer 14

Ok

Answer 15

Option C :

reflected over the x-axis and rotated 90� counterclockwise

reflection over x-axis :
takes "D" from 2nd quadrant to 3rd quadrant

rotating 90 degrees counterclockwise :
takes it to 4th quadrant

Answer 16

so, OptionC is ur correct answer.

Answer 17

Wow thank you so much , I think what was messing me up was the fact of counterclockwise and clockwise . Thanks for the help =)

Answer 18

it can... takes practice.... u wlc :)