Question

POH Gandalf the Grey started in the Forest of Mirkwood at a point with coordinates (-1 -1) and arrived in the Iron Hills at the point with coordinates (1,4). If he began walking in the direction of the vector v = 5i + 1j and changes direction only once, when he turns at a right angle, what are the coordinates of the point where he makes the turn. 2.444

Answer 1

(-1,-1) not (ay) = sitj tccry) Pet co-ordinates of Bex,y) be Carys. Then [(x+1) € + ly+14]. [61- x) +14-yj] =0 3) (-812) + (4-y)(1+14) = 0 =) 1-342+4-+44-y2=0 =) y++-34-5=0 Also, +B) 11 ñ . so Rex + =0. [{*+1) € +4y+195 ][si+j370 - 56x+1) R - 5(y+1)&=0 = (2+1)-(4+1) =0 =) Rey to y² + y ²-3y=520 - 242_34.550 = 24 ²5y +2y 5=0 ->@y-5) (y+1) zo - y = 5/2,-1. when y=85, d = 6, when y=-1, dan) But if x=y=-1, then we get a so our point B is ($, &