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##### Asked by: Qadeer Barbia

science space and astronomy# How do you construct a perpendicular line with a compass?

**Construct: a line through P perpendicular togivenline.**

- STEPS:
- Place your
**compass**point on P and swing an arc ofanysize that crosses the**line**twice. - Place the
**compass**point on one of the two locationswherethe arc crossed the**line**and make a small arc belowthe**line**(on the side where P is not located).

Similarly, you may ask, how do you construct a perpendicular line through a point?

**To drop a perpendicular from a point to a line**

- open the compass a distance larger than theperpendiculardistance from the point to the line, and scribe an arcintersectingthe line at two points.
- Call the two points B and C. Scribe arcs from B and C ofthesame radius on the other side of the line from A.

**lines are perpendicular if**andonly

**if**their slopes are negative reciprocals. To findtheslope, we must put the equation into slope-intercept form, ,whereequals the slope of the

**line**.

Keeping this in consideration, how do you construct a parallel line?

**Method 1** **Drawing Perpendicular Lines**

- Locate the given line and the given point.
- Draw an arc that intersects the given line at twodifferentpoints.
- Draw a small arc opposite the given point.
- Draw a another small arc intersecting the previous one.

**Parallel** lines have the same slope and willneverintersect. **Parallel** lines continue, literally,foreverwithout touching (assuming that these lines are on the sameplane).On the other hand, the slope of **perpendicular** linesare thenegative reciprocals of each other, and a pair of theselinesintersects at 90 degrees.