# 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 \$\displaystyle A(3,2)\$ and any point \$\displaystyle P(x,y)\$

Code:

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

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

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

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