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To erect a perpendicular to a given line at a given point on the line. |
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To erect a perpendicular to a given line at a given point on the line. |
| Given: Point P on line AB |
| Required: To erect a perpendicular to line AB at P. |
| Procedure: |
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 With P as a center,
use the compass tool to construct a circle intersecting AB at C and D. |
| With C as center and with a radius
greater than 1/2 CD, use the compass tool to construct a circle. |
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Label any point on this circle G. |
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Use the segment command under the construct menu and
construct a segment congruent to CG, the circle radius. |
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Use the circle by center + radius command under the construct menu and construct a circle with D as the center and
radius congruent to segment CG. |
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Label the intersection of the above two circles as
point E. |
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Use the segment command under the construct menu and construct segment PE. |
| PE is the required perpendicular. |
| Proof: |
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Since radii of the same circle or equal
circles are equal, P and E are equidistant from C and D. |
PE 
CD |
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PE
AB (Two points each
equidistant from the extremities of a line segment determine the
bisector of that line segment.) |
| Sketch: On the sketch below, drag points A, B, or P and observe what happens. What condition is not being met that makes the perpendicular disappear as P gets closer to B? |
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This page uses JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial use. perpendicular to point on a line |
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