1. ## Trigonometry Question

Being a triangle and a point inside .
Find the coordinates of the points and on the sides of , in function of the coordinates of the points and , in a way that divides the line segment in half.
(Tip: Consider the point to be on the origin of the coordinates system and point to be on the axis.)

2. ## Re: Trigonometry Question

Hey Don,
Refer to the figure attached. Choose x-axis along $\displaystyle AB$ and y-axis along $\displaystyle AC$ with the origin at $\displaystyle A$.

$\displaystyle Q,R$ can be interchanged.

Case 1.
$\displaystyle QR$ on sides $\displaystyle AB$ and $\displaystyle AC$ we have $\displaystyle Q=(2\alpha,0)$, $\displaystyle R=(0,2\beta)$. With the additional condition that $\displaystyle 0 \le \alpha \le \frac{b}{2}$, $\displaystyle 0 \le \beta \le \frac{c}{2}$

Case 2.
$\displaystyle QR$ on sides $\displaystyle AC$ and $\displaystyle BC$ we have the abscissa of $\displaystyle Q$ is $\displaystyle 0$ and hence abscissa of $\displaystyle R$ has to be $\displaystyle 2\alpha$. Let the ordinate of $\displaystyle Q$ be $\displaystyle \gamma$ then we have ordinate of $\displaystyle R$ has to be $\displaystyle 2\beta-\gamma$ and it has to satisfy the line equation $\displaystyle \frac{y}{x-b} = -\frac{c}{b} \implies \gamma = -\frac{c(2\alpha - b)}{b}$ with the additional bound constraints $\displaystyle 0 \le \alpha \le \frac{b}{2}$ and $\displaystyle 0 \le \gamma \le c$

Case 3.
Can be done on similar lines of Case2.

Now use the rotational matrix to translate to the Rectangular Cartesian Co-ordinates.

~Kalyan.