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Question 1174470: Find the distances of the point (4,-2) from the line 2x+3y-6=0
Answer by ikleyn(52855)   (Show Source):
You can put this solution on YOUR website! .
There is a remarkable formula to calculate the distance from a given point to a given straight line in a coordinate plane.
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.
Your straight line is 2x + 3y - 6 = 0. The point is (4,-2)
Substitute the given data a= 2, b= 3, c= -6, = 4, = -2 into the formula to get the distance under the question
 =  =  =  = 1.1094 (approximately).
Answer. The distance is = 1.1094 (approximately).
Solved.
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