Distance of a Point from a Line
Examples, solutions, videos, activities, and worksheets that are suitable for A Level Maths.
How to find the shortest distance from a point to a given line?
The shortest distance between a point and a line is a perpendicular line segment.
- Find the slope of the perpendicular line formed from the point. (Negative reciprocal from the given line)
- Find the equation of the line with the shortest distance y = mx + b. (Use the slope you found in step 1 and substitute the values of the point to find the b value)
- Find the point of intersection of the two lines by solving the systems of two equations.
- Find the length of the line segment by using the point of intersection from step 3 to the given point.
The following diagram gives the steps to find the shortest distance between a point and a line. Scroll down the page for more examples and solutions.
Shortest Distance from a Point to a Line Part 1
The following lesson looks at Shortest Distance from a Point to a Line. This is the first part of 3 videos
Shortest Distance from Point to a Line Part 2
The following lesson looks at Shortest Distance from a Point to a Line. This video continues from Part 1.
Shortest Distance From a Point to Line Part 3
The following lesson looks at Shortest Distance from a Point to a Line. This video is the final part continuing from part 2
Shortest Distance between a Point and Line using Equations of Lines
Use equations of lines
- Find equation of second line (slope is negative reciprocal)
- Find point of intersection
- Use distance formula
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