SOLUTION: How far is the point (4,1) from the line y= -2x+3?

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Question 1128794: How far is the point (4,1) from the line y= -2x+3?
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.
Use the general formula:


    the distance from the point (p,q) to a straight line ax + by + c = 0  is

              d = abs%28ap+%2B+bq+%2Bc%29%2Fsqrt%28a%5E2+%2B+b%5E2%29.



Regarding this formula, see the lesson  The distance from a point to a straight line in a coordinate plane  in this site.


In your case, the equation of the straight line is 2x + y - 3 = 0, so the distance is

    d = abs%282%2A4+%2B+1%2A1+-+3%29%2Fsqrt%283%5E2%2B1%5E2%29 = 6%2Fsqrt%2810%29 = %286%2Asqrt%2810%29%29%2F10 ~ 1.897367 (approximately).