Question 1066041
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Let the straight line in a coordinate plane is defined in terms of its linear equation 


{{{a*x + b*y + c = 0}}},                       (1)


where &nbsp;<B>a</B>, &nbsp;<B>b</B> and &nbsp;<B>c</B> &nbsp;are real numbers, &nbsp;and let &nbsp;<B>P</B> = <B>P</B>({{{x[0]}}},{{{y[0]}}})&nbsp; is the point in the coordinate plane 
with the coordinates &nbsp;{{{x[0]}}}, &nbsp;{{{y[0]}}}. &nbsp;Then the distance from the point &nbsp;<B>P</B>&nbsp; to the straight line &nbsp;(1)&nbsp; is equal to&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;


{{{d}}} = {{{abs(a*x[0] + b*y[0] + c)/sqrt(a^2 + b^2)}}}.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(2)


See the lesson 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Vectors/The-distance-from-a-point-to-a-straight-line-in-a-coordinate-plane.lesson>The distance from a point to a straight line in a coordinate plane</A>

in this site.


By applying this formula, you get


d = {{{(abs(30*9 - 15*18 - 75))/sqrt(30^2 + (-15)^2)}}} = = {{{75/sqrt(1125)}}} = {{{sqrt(5)}}} = 2.236 (approximately).



It is very useful to know this formula and to apply it properly and correctly when it is needed.

It will save you a lot of efforts and time.