# Example 3

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.

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