Gandalf the Grey started in the Forest of Mirkwood and make a right angle turn

Question

Gandalf the Grey started in the Forest of Mirkwood at a point with coordinates (0, -3) and arrived in the Iron Hills at the point with coordinates (2, 2). If he began walking in the direction of the vector v=3i+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 understand what the problem is asking but don't know how to get the final answer

Answer 1

What is the slope of the line for Gandalf's walk?

What would be slope be of the line at the right turn?

Determine the equations of the two lines.

Deteremine the point of interesection of the two lines.

Answer the question.