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

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° is given by   x−2cos⁡45∘=y−3sin⁡45∘=rCo-ordinates of any point on this line are  2+rcos⁡45∘,3+rsin⁡45∘ or, 2+r2,3+r2If this point lies on the line 2x-3y+9=0, then    4+r2−9−3r2+9=0⇒r=42Hence, required distance =42 units .