SOLUTION: Find the distance from point A(−14, 5) to the line −x+2y = 14. Round your answer to the nearest tenth.

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Question 1100406: Find the distance from point A(−14, 5) to the line −x+2y = 14. Round your answer to the nearest tenth.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
There is a beatiful formula to find the distance from the given point to the given straight line in a coordinate plane.

This formula is: 

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


        a*x + b*y + c = 0,


    where  a,  b and  c  are real numbers,  and let  P = P(,)  is the point in the coordinate plane 
    with the coordinates  ,  .  Then the distance from the point  P  to the straight line is equal to


        d = .


See the lesson  The distance from a point to a straight line in a coordinate plane  in this site.


So, in your case  a= -1,  b= 2,  c= -14   (after moving  "c"  from the righ side to the left),  = -14,  = 5.

Substituting to the formula gives you the distance

d = = = = = = 4.5 (approximately; rounded to the nearest tenth).


Solved.


Again,  for the proof of the formula and other details look into the above referred lesson.


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