Constructing Parallel Lines

Recall that parallel lines are coplanar lines that do not intersect.  There is a constant distance between them.  You will use this property to construct a line parallel to a given line through a given point on the coordinate plane.

Point N is given in Quadrant I and we are asked to draw a line through this point parallel to the x-axis.

Step 1. Draw two arbitrary points G and H on x-axis. Then, using a ruler, draw a line from G through N, as shown in the figure below.  In this step, you have constructed a transversal that will cut through the axis and the line you are about to construct.

Step 2. By placing a compass at point G, draw two arcs with the same radius. Let F and H be the points of intersection of these curves with GN and x-axis.

Step 3. Create an equal angle to FGH at N such that one side is on GN. The horizontal side of this angle, LN, is parallel to x-axis.

All lines that are parallel to the x-axis are horizontal, meaning that they go from left to right.

All lines that are parallel to the y-axis are vertical, meaning that they go up and down.