What is the distance of the point (3,2) from the line 3x - 8y = 18

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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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