# how to translate point along given vector...

• Oct 28th 2013, 04:47 PM
wilbsy
how to translate point along given vector...
Attachment 29610
here's the situation...

the radius of the red circle is a given constant. point A can exist anywhere in any quadrant, but is always given... how would i calculate the coordinates of point B (the intersection of vector C with red circle).

thanks!
• Oct 28th 2013, 05:05 PM
Plato
Re: how to translate point along given vector...
Quote:

Originally Posted by wilbsy
Attachment 29610
the radius of the red circle is a given constant. point A can exist anywhere in any quadrant, but is always given... how would i calculate the coordinates of point B (the intersection of vector C with red circle).

Suppose that the coordinates of $A: (x,y)$.
Suppose that $x\cdot y\ne 0$ then
$\Theta=Arg(x,y) = \left\{ {\begin{array}{{lr}} {\arctan \left( {\frac{y}{x}} \right),}&{x > 0} \\ {\arctan \left( {\frac{y}{x}} \right) + \pi ,}&{x < 0\;\& \;y > 0} \\ {\arctan \left( {\frac{y}{x}} \right) - \pi ,}&{x < 0\;\& \;y < 0} \end{array}} \right.$

Then $\Theta$ is the measure of the angle the vector $\vec{C}$ makes with the positive $x\text{-axis}~.$

Now the coordinates of $B: (r\cos(\Theta),r\sin(\Theta))$ where $r$ is the radius of the circle.