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A person standing at the junccction 9CROSSING0 of two sssstraight paths,represented by the equatins 2x -3y +4=0 and 3x +4y +5 =0 wants to reach the path wwwwhose equation is 6x-7y+8=0 in the least time.find the equation of the path that he should follow.
find coordinates at junction of first two straight paths:
2x -3y +4=0
3x +4y +5 =0
(x,y) coordinates at junction:(-31/17,2/17)
slope of path to reach
shortest path would be a perpendicular line from this line to coordinates of the junction
slope of perpendicular line =-7/6 (negative reciprocal)
solve for b using coordinates of the junction
Equation of path to follow:
see graph below: