SOLUTION: Find the shortest distance from the given point (-3,0) to the given line x-y=-10

You want to find the distance from the point (-3,0) to the given straight line  x - y + 10 = 0.


There is a remarkable formula which ideally suits for this need.


    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 = (,) be the point in the coordinate plane. 

    Then the distance from the point P to the straight line is equal to

        d = .


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


Substitute the given data  a= 1, b= -1, c= 10,   = -3,  = 0  into the formula to get the distance under the question


     =  =  = 4.95 units  (approximately).


Answer.  The distance under the question is 4.95 units  (approximately).