Construct Perpendicular Lines

High School Math based on the topics required for the Regents Exam conducted by NYSED. How to construct a perpendicular line to a point and a perpendicular line through a point not on a line?

The following diagrams show how to construct a perpendicular through a point not on the line and a perpendicular through a point on the line. Scroll down the page for more examples and solutions.

 

Constructing a Perpendicular
The shortest distance between a point not on a line and a line is along the perpendicular to the line. Constructing a perpendicular to a line uses the same process as constructing the perpendicular bisector of a line segment, but with one additional step. The first step is to swing an arc from the point and intersect the line in two places, which creates a segment that can be bisected.

Constructing Perpendicular lines
The video explains how to construct a perpendicular line to a point and a perpendicular line through a point not on a line

Perpendicular Line(1) Construction
How to use a compass and straightedge to construct a perpendicular line through a point on the line?

Perpendicular Line(2) Construction
How to use a compass and straightedge to construct a perpendicular line through a point not on the line?

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