SOLUTION: What is the value of k if point P(k, k square root 3 ) is 4 units from the line 5x+3y=12?

There is a remarkable formula for the distance from the point (p,q) to the line ax + by + c = 0 in a coordinate plane.


This formula is


    d = .


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


In our case  p = k,  q = , a= 5, b= 3, c= -12.


So,  d =  = ,


and your equation for the value of "k" is 


 = 4.


Simplify it

 = .


There are TWO solutions for k:


1)  k = ,   and


2)  k = .