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December 2, 2016
Posted by **jessica** on Monday, February 23, 2009 at 5:15pm.

i guess it is (-1.6) is it?

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**Damon**, Monday, February 23, 2009 at 5:21pmThat point is in quadrant 4, down to the right.(1 unit right of -y axis and 6 down)

Spin it 90 degrees and it ends up above the x axis a distance 1 and a distance 6 right of the origin

so I get

(1,6) - transformation -
**Reiny**, Monday, February 23, 2009 at 5:24pmno,

did you make a sketch?

I see it as (-6,-1)

Proof: slope of original line = (-6-0)/(1-0) = -6

slope of new line = (-1-0)/(-6-0) = 1/6

they are negative recipricals so they form a 90º angle

also you can verify that their lengths are the same.

btw, are you using a rotation matrix ?

what grade level is this in ?

R(theta)=

│costheta -sintheta │

│sintheta costheta] │ - transformation -
**jess**, Monday, February 23, 2009 at 5:31pmi am in grade 11 but this stuff is from grade 10. i am a new student and have not studied it back in my country. the paper is due tomorrow and i don't have a clue how to do it.... the substitute handed us the paper today. so i cannot even ask my teacher till tomorrow....

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**Reiny**, Monday, February 23, 2009 at 5:39pmyour best bet might be to make a sketch on graph paper, and use your intuition.

Notice that the x and y values contain the same numbers, except their signs might have switched as well as their positions, (-1,6) became (-6,-1)

in general (a,b) becomes (-b,a) after a 90º counter-clockwise rotation and (b,-a) for a clockwise rotation. - transformation -
**jess**, Monday, February 23, 2009 at 5:49pmthank you so much....i think i got it. thanks again!!!

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**Damon**, Monday, February 23, 2009 at 6:10pmSorry, I made a typo

one up and 6 right is

(6,1)

which you can also get by he matrix operation

0 -1

1 +0

times your (1,-6) vector - transformation -
**Reiny**, Monday, February 23, 2009 at 6:19pmDamon, I think she wanted to rotate counter-clockwise, you went clockwise

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**Reiny**, Monday, February 23, 2009 at 6:46pmDamon, I apologize

You went the correct way, I messed up and went the wrong way. - transformation -
**jess**, Monday, February 23, 2009 at 6:55pmthank you both....so the correct answer is (6,1) Thanks!!! :)

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**Damon**, Tuesday, February 24, 2009 at 4:13amI cheated and checked the matrix in my thick math book :)