EMAT 6700

by Brad Simmons

Perpendicular Lines through a Point on the Line.

Use geometer's sketchpad to construct a line perpendicular to a given line and passing through a given point on the line.

1. Start with line n and point C on line n.   

2.  Select line n.  Construct a point on the line and name it point A.  Select point C and point A.  Construct segment AC.

3.  Select point C and segment AC.  Construct circle by center and radius.  Select line n and circle C.  Construct points of intersection.  Name the other point of intersection point B.

4. Select circle C and segment AC.  Hide the objects.  Select line n.  Construct a point on the line and name it point D.  Move point D so it is between point C and point A.  Select point B and point D.  Construct segment BD.

5.  Select point B and segment BD.  Construct circle by center and radius.  Select point A and segment BD.  Construct circle by center and radius.

6.  Select circle A and circle B.  Construct a point of intersection and name it point E.

7. Select circle A, circle B, segment BD, and point D. Hide the objects.  Select point E and point C.  Construct line CE.

8. By construction, line EC is perpendicular to line n at point C.  Measure angle ECA and confirm that it has a measure of 90 degrees.


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