Question

A person standing at the junction of two straight paths represented by equation 2x-3y+4=0 and 3x+4y-5=0 wants to reach the path whose equation is 6x-7y+8=0 in the least time . Find equation of path that he should follow

Answer 1

Heya!!!

Least distance would be only the perpendicular distance.

Let's Find out the co-ordinates of junction point ist.

2x -3y = -4 .... equation ( i )

3x + 4y = 5 .... equation ( ii )

Multiply equation ist by 3 and second by 2

6x - 9y = -12

6x + 8y = 10

- - -
___________

-17y = -22

y = 22/17 And x = -1/17

Let the length of path be d

d = {6( -1/17 ) -7 ( 22/17 ) + 8 }/√ (6² +7²)

d = 24/ 17√113