Distance between point and line

The  exercise appears under the Algebra I Math Mission. This exercise finds the perpendicular distance from a line to a point.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the exact distance: This problem provides a line and a point on a coordinate plane. The student is asked to find the exact distance from the point to the line and provide the answer as a simplified radical.Dbpal1.png

Strategies
Knowledge of simplifying radicals and the distance to a line formula would ensure success on this exercise. There are alternative methods to find the distance.
 * 1) One can find the equation of a line perpendicular to the given line through the point and see where those lines intersect. That would be the shortest distance.
 * 2) A formula for this is $$ abs(Ax_0+By_0+C)/sqrt(A^2+B^2) $$ if the line is transferred into point-slope form.
 * 3) A calculator is not extremely useful here as the answer need to be written as an exact radical if needed.
 * 4) Commonly the line is horizontal or vertical which makes the problem must faster to complete.
 * 5) The perpendicular distance can be visualized without calculation occasionally, increasing speed.

Real-life Applications

 * 1) In nature objects often take the path of least resistance, which includes finding shorted routes where possible.