Perpendicular Lines
Two lines that intersect to form right angles.
Perpendicular lines are two lines that intersect at a right angle (90 degrees). The point of intersection is called the perpendicular or the right angle. When two lines are perpendicular, they form four right angles at the point of intersection.
There are a few characteristics that perpendicular lines have:
1. Opposite reciprocal slopes: When two non-vertical lines are perpendicular, their slopes are opposite reciprocals of each other. This means that if one line has a slope of m, then the other line will have a slope of -1/m. For example, if one line has a slope of 2, then the other line will have a slope of -1/2.
2. Intersect at right angles: As mentioned earlier, perpendicular lines intersect at a right angle. This means that the angle between the two lines is 90 degrees.
3. Symmetry: Perpendicular lines are symmetric around the point of intersection, which means that if one line is reflected over the other, the resulting lines will still be perpendicular.
4. Distance: If a point is located on one of the lines, then its distance to the other line is the shortest distance between the two lines. This distance is measured along a line that is perpendicular to both lines.
In geometry, perpendicular lines are used in a variety of contexts, ranging from finding the equations of lines to constructing 90-degree angles. It is important to know how to identify and work with perpendicular lines in order to succeed in geometry and other math courses.
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