How to rotate points given in square grid?

Question

I really hope you can see this picture. So My question is 1) If the figure is rotated 90 degrees counter clock wise about Point O, then: $$a. G to _________$$ $$b. _________ to P $$ How would i rotate i don't even know how to start this?

Answer 1

Imagine a line from $O$ to $G$ and $O$ to $P$. What points form a line with $O$ that is $90$ degrees to these lines?

Taking the direction of the rotation into account, then you would get $$G \text{ to } E$$ and $$N \text{ to } P$$

Answer 2

Get out a piece of trace paper (or such) and trace the image you have shown us. Rotate it $90^\circ$ and see what you get.

As far as coordinates go, a rotation of $90^\circ$ tranforms the point with coordiates $(x,y)$ to a point with coordinates $(-y, x)$. Using $\overleftrightarrow{OF}$ as the $x$-axis and $\overleftrightarrow{ON}$ as the $y$-axis, $G(1,-1)$ becomes the point $E(1,1)$. Let $W(x,y)$ be the point that gets sent to $P(-1,0)$. Then we must have $(-y,x) = (-1,0)$ So $(x,y)=N(0,1)$.