EMAT 6700

Perpendicular Lines through a Point not on the Line.

Use geometer's sketchpad construct a line perpendicular to a given line and passing through a given point that is not on the given line.

1. Start your sketch with line m and point Z not on line m.

2.  Construct a point A on the opposite side of line m as point Z.  Select point Z and point A.  Construct segment AZ.

3.  Select point Z and segment AZ.  Construct circle by center and radius.  Select line m and circle Z.  Construct points of intersection and name them point X and point Y.

4.  Select circle Z, point A,  and segment AZ.  Hide the objects.  Select line m.  Construct a point on the line and name it point C.

5.  Move point C so it is closer to point Y than is to point X.  Select point X and point C.  Construct segment CX.

6.  Select point X and segment CX.  Construct circle by center and radius.  Select point Y and segment CX. Construct circle by center and radius.

7.  Select circle X and circle Y.  Construct point of intersection and name it point D (this point should be on the opposite side of line m as point Z).

8.  Select circle X, circle Y, segment XC, point C, and the other point of intersection of the circles that is on the same side of line m as point Z. Hide the objects.  Select point Z and point D.  Construct line DZ.

9. By construction line ZD is perpendicular to line m.  Go ahead now and construct the point of intersection of line m and line ZD and name it point G.  Measure angle ZGY and confirm that it has a measure of 90 degrees.

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