Question

Gandalf the grey started in the forest of mirkwood at a point pp with coordinates (−2,1)(−2,1) and arrived in the iron hills at the point qq with coordinates (-1, 6). if he began walking in the direction of the vector v=3i+2jv=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?

Answer 1

travel direction 3i + 2j, slope = 2/3.
We have slope and a point (-2,1) this gives us a line equation:
 LINE BEFORE THE TURN, EQUATION: y = (2/3)x + 1

The point of intersection of the two lines:
1) through (-2,1) with slope 2/3 and;
2) through (-1,6) with slope 3/2.