Find the point on the given line that is closest to the given point.
Note: Drag the blue point to try a different problem.

Find the line perpendicular to the given line that passes through the given point.

Identify the slope of the given line.

Find the opposite reciprocal of the slope of the given line.

Substitute the opposite reciprocal for in the point-slope form of a linear equation.

Substitute and from the given point into the equation for and .

Simplify the equation.

Find the intersection between the two lines by setting the given equation equal to the equation of the perpendicular line, then solve for .

Substitute the value of back into the given equation to find the value of .

Calculate the distance between the two points using the distance formula.

This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit www.walch.com for more information on their resources.