# transformation

• Jun 9th 2011, 08:50 PM
Veronica1999
transformation
A quarter turn is a 90 degree rotation. If the counterclockwise quarter-turn centered at (3,2) is applied to (7,1) what are the coordinates of the image? What are the image coordinates when this transformation is applied to a general point (x,y)?

I have (4,6) but i can't get the second one.

Pls find attached work.i have found a vector pattern for the transformation
• Jun 9th 2011, 09:57 PM
Soroban
Hello, Veronica1999!

Quote:

A quarter turn is a 90 degree rotation.
If the counterclockwise quarter-turn centered at (3,2) is applied to (7,1),
. . what are the coordinates of the image?
What are the image coordinates when this transformation
. . is applied to a general point (x,y)?

We have the point $A(3,2)$ and any point $P(x,y)$

Code:

|                y-2
|            Q * - - *
|                    :
|                    :
|                    : x-3
|                    :
|                    :
|                    :P
|                    *(x,y}
|                *  :
|            *      :y-2
|        *          :
|  A * - - - - - - - *
|  (3,2)  x-3
--+------------------------
|

Going from $A$ to $P$, we move $x\!-\!3$ units right and $y\!-\!2$ up.

Going from $P$ to $Q$, we move $x\!-\!3$ units up and $y\!-\!2$ left.
. . (I hope you understand why.)

Therefore, point $Q$ is at: . $(x\!-\!y\!+\!2,\:x\!+\!y\!-\!3)$