thee distance of the point (2,3) from the lne 2x-3y+9=0 measured along a line x-y+1=0 is - Maths - Straight Lines

Question

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

Rajat Sethi · Accepted Answer

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Slope of line 2x - 3y +9 =0 is m1 = 23Slope of line x - y +1 =0 is
m2 = 1Now,angle between the two lines is tanθ = m2 - m11
+m1m2 = 1 - 231+1×23= 15sinθ = 126Now,perpendicular
distance of(2,3) from 2x - 3y +9=0 isp =2×2 -3×3 + 922
+ 32=413

Now distance along the given line = psinθ = 413×26 = 42
units