Perpendicular Lines
two or more lines that cross at right angles
Perpendicular lines are two lines that intersect each other at a 90-degree angle. This intersection point is called the point of intersection, or the right angle. The slopes of perpendicular lines are opposite reciprocals of each other.
To find if two lines are perpendicular, we can calculate their slopes using the slope formula, which is:
m = (y2 – y1)/(x2 – x1)
If two lines have slopes m1 and m2, then they are perpendicular if and only if
m2 = -1/m1
For example, consider two lines with equations y = 2x + 1 and y = -1/2x + 3.
The slope of the first line is m1 = 2, and the slope of the second line is m2 = -1/2. To check if they are perpendicular, we use the formula m2 = -1/m1:
-1/2 = -1/2
Since the slopes are opposite reciprocals, we can conclude that the lines are perpendicular.
Perpendicular lines are commonly used in geometry and trigonometry to find angles, draw shapes, and solve problems involving right triangles. They are also used in real life situations, such as construction, architecture, and engineering.
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