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A line is made of an infinite number of points and extends in both directions. By distance of the point (3,2) from the line 3x - 8y = 18 it is assumed you are referring to the shortest distance between the two or the length of the perpendicular line segment dropped from the point (3,2) to the line 3x - 8y = 18.
The perpendicular distance of (A, B) from a line ax + by + c = 0 is given by `D = |a*A + b*B + c|/sqrt(a^2 + b^2)` ` ` .
Here, A = 3, B = 2, a = 3, b = -8 and c = -18.
Substituting these values in the formula for distance gives:
D =`|3*3 - 8*2 -18|/sqrt(3^2 + 8^2)` ` `
= `|9 - 16 - 18|/sqrt (9 + 64)` ` `
= `25/sqrt 73`
The perpendicular distance of the point (3,2) from the line 3x - 8y = 18 is `25/sqrt 73 ` ` `
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