When we talk about the distance from a point to a line, we mean the shortest distance. If you draw a line segment that is perpendicular to the line and ends at the point, the length of that line segment is the distance we want. In the figure above, this is the distance from C to the line.

There are many ways to calculate this distance. In this volume, four methods are described:

Method 1. When the line is horizontal or vertical

• See Distance from a point to a horizontal / vertical line

Method 2. Using two line equations

• See Distance from a point to a line using line equations

Method 3. Using trigonometry

• See Distance from a point to a line using trigonometry

Method 4. By formula

• See Distance from a point to a line using a formula

Limitations

In the interest of clarity in the applet above, the coordinates are rounded off to integers and the lengths rounded to one decimal place. This can cause calculatioons to be slightly off.

For more see Teaching Notes

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Other Coordinate Geometry topics

• Introduction to coordinate geometry
• The coordinate plane
• The origin of the plane
• Axis definition
• Coordinates of a point
• Distance between two points

• Introduction to Lines
  in Coordinate Geometry
• Line (Coordinate Geometry)
• Ray (Coordinate Geometry)
• Segment (Coordinate Geometry)
• Midpoint Theorem

• Distance from a point to a line
• - When line is horizontal or vertical
• - Using two line equations
• - Using trigonometry
• - Using a formula

• Intersecting lines

• Cirumscribed rectangle (bounding box)
• Area of a triangle (formula method)
• Area of a triangle (box method)
• Centroid of a triangle
• Incenter of a triangle
• Area of a polygon
• Algorithm to find the area of a polygon
• Area of a polygon (calculator)
• Rectangle
• Definition and properties, diagonals
• Area and perimeter
• Square
• Definition and properties, diagonals
• Area and perimeter
• Trapezoid
• Definition and properties, altitude, median
• Area and perimeter
• Parallelogram
• Definition and properties, altitude, diagonals

• Print blank graph paper