Hello klaus113

Welcome to Math Help Forum! Originally Posted by

**klaus113** Hi

Please help me. I want to know how to find the coordinates of a circle after they have been rotated some degrees.

One problem I read wrote this:

"Shown in the standard (x,y) coordinate plane below, pint P (6,6) is rotated 90 degrees clockwise about the orgin (2,3). What are the coordinates of P after the rotation has been complete?"

I know the answer is (5,-1), but I don't know why that is the answer or how to solve the problem for other questions!

Think about any point whose coordinates are $\displaystyle (x_1,y_1)$ - see the attached diagram. Its horizontal and vertical distances from $\displaystyle (2, 3)$ are $\displaystyle x_1-2$ and $\displaystyle y_1-3$, respectively. After a rotation through $\displaystyle 90^o$ clockwise about this point, these will be the vertical distance below and the horizontal distance to the right of this point.

So the coordinates of the image of $\displaystyle (x_1,y_1)$ after this rotation are$\displaystyle (2+y_1-3, 3 -[x_1-2])$; i.e. $\displaystyle (y_1-1, 5-x_1)$

This gives the general formula you're looking for, and confirms that $\displaystyle (6,6) \mapsto (5, -1)$.

Grandad