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.