When two lines intersect each other at right angles, we say they are perpendicular. This means the angle they form at the intersection point is 90 degrees. Let's learn how to construct a perpendicular line to an existing line through a point not on the line.
Construction of Perpendicular Line Through a Point - Testbook
Last Updated on May 22, 2024
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Building a Perpendicular Line to a Given Line Through a Point Not on the Line
Suppose we have a line segment AB and a point P that is not on line segment AB.
We want to construct a line that is perpendicular to line AB and passes through point P.
Construction Steps
- Step 1: Starting with point P as the center, draw an arc that intersects line segment AB at two distinct points. Let's call these points X and Y.
- Step 2: Next, use X as the center and draw an arc on the side opposite point P. Also, use Y as the center and the same radius to draw another arc on the side opposite point P. The point where these two arcs intersect is point M.
- Step 3: Draw a line from point P to point M. This line PM is the perpendicular line to line segment AB that we wanted to construct.
To verify that line segment PM is indeed perpendicular to line segment AB, connect points M, P, X, and Y as shown below:
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Frequently Asked Questions
What does it mean when two lines are perpendicular?
Two lines are perpendicular when they intersect each other at a right angle, or 90 degrees.
How to construct a perpendicular line to a line segment from an external point?
To construct a perpendicular line to a line segment from an external point, follow these steps: 1. With the external point as the center, draw an arc cutting the line segment at two distinct points. 2. With these points as centers, draw two arcs on the opposite side of the given point to intersect each other. 3. Join the intersection point of these arcs to the given point. This line is the required perpendicular line.
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