I am given this Question of
Gandalf the Grey started in the Forest of Mirkwood at a point with coordinates (-2, -3) and eventually arrived in the Iron Hills at the point with coordinates (0, 0). If he began walking in the direction of the vector v=4i+2j and changes direction only once, when he turns at a right angle, what are the coordinates of the point where he makes the turn.
I have absolutely no idea where I would start. I've tried using the distance formula, tried finding the slope and plugging in the points and using the inverse of the slope to find out the x and y but nothing works
Gandalf wants to travel from $(-2, -3)$ to $(0,0)$.
He is traveling along the direction $(4,2)$ and $(-2,4)$.
Hence we just have to solve for $$(-2,-3) + x(4,2) + y(-2,4) =(0,0)$$
The turning point is $(-2,-3)+x(4,2)$.
Solving for $x,y$ is just solving two linear equations in $2$ unknowns and the solution is unique.