Gandalf the Grey started in the Forest of Mirkwood at a point with coordinates (

Question

Gandalf the Grey started in the Forest of Mirkwood at a point with coordinates (-1, -3) and arrived in the Iron Hills at the point with coordinates (1, 0). If he began walking in the direction of the vector V=3i+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. ( , )

Explanation / Answer

he began walking in the direction of the vector V=3i+1j =>he started walking along vector (3-(-1))i+(1+3)j=4i+4j line joining points (3,1)and (-1,-3) is y-1=4/4(x-3) =>y=x-2...............1 slope of a line which is perpendicular to this line is = -1/1=-1 equ of line which is perpendicualar to 1 and passing through (1,0) is y-0=-1(x-1) =>y=-x+1.......2 1 and 2 will intersect at y=x-2 and y=-x+1 =>2y=-1 y=-1/2 x=3/2 this is required point

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