The distance of the point (2,3) from the line 2 x-3 y+9=0 measured along a line x-y+1=0 is

Step-by-step solution

The slope of the line x-y+1=0 is 1 . So, it makes an angle of 45^ with x -axis. The equation of a line passing through (2,3) and making an angle of 45^ x-2 45^ = y-3 45^ =r Coordinates of any point on this line are (2+r 45^ , 3+r 45^ ) or, (2+ r 2 , 3+ r 2 ) If this point lies on the line 2 x-3 y+9=0 , then 4+ 2 r-9- 3 r 2 +9=0 r=4 2 Alternate Method Since the point (2,3) lies on the line x-y+1=0 . Therefore the distance from (2,3) to the line 2 x-3 y+9=0 along the line x-y+1=0 is equal to the distance between the