Creatives Common | How to Construct a Line Parallel to a Given Line Through a Given Point?
Channel: Creative Common Genuine Videos
Date: 2019-08-22

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How to Construct a Line Parallel to a Given Line Through a Given Point

Parallel lines are lines that are equidistant at all points and would never touch if they went on forever.1 Sometimes you may be presented with one line and need to create another line parallel to it through a given point. You might be tempted to simply take a straight edge and draw a line that seems right  however, you could not be sure that the line you constructed was technically parallel. Using geometry and a compass, you can plot additional points that will ensure the line you construct is truly parallel. 

Drawing Perpendicular Lines Locate the given line and the given point.

 The point will not be on the given line, and can be above or below it. Label the line m{\displaystyle m} and the point A{\displaystyle A}.  Draw an arc that intersects the given line at two different points.

 To do this, place the compass tip on point A{\displaystyle A}. Open the compass so that it is wide enough to reach beyond line m{\displaystyle m}, then draw an arc that sweeps across the line at points B{\displaystyle B} and C{\displaystyle C}. Draw a small arc opposite the given point.

 To do this, open the compass a little wider. Set the compass tip on point B{\displaystyle B}, and draw an arc that sweeps directly across from point A{\displaystyle A}. If the given point is above the line, you should draw this arc below the line. If the given point is below the line, you should draw this arc above the line.  The arc does not have to be very long, as long as part of it falls directly under the given point. Draw a another small arc intersecting the previous one.

 To do this, keep the compass set to the same width. Set the compass tip on point C{\displaystyle C} and draw an arc that intersects the previous small arc. Label this point D{\displaystyle D} Draw a line that connects the given point and the intersection of the two small arcs.

 Label this line line n{\displaystyle n}. Line n{\displaystyle  Parallel lines are lines that are equidistant at all points and would never touch if they went on forever.1 Sometimes you may be presented with one line and need to create another line parallel to it through a given point. You might be tempted to simply take a straight edge and draw a line that seems right  however, you could not be sure that the line you constructed was technically parallel. Using geometry and a compass, you can plot additional points that will ensure the line you construct is truly parallel. 

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