Understanding Perpendicular Lines: Definition, Examples, and Applications

perpendicular lines

Perpendicular lines are two lines that intersect each other at a right angle or 90 degrees

Perpendicular lines are two lines that intersect each other at a right angle or 90 degrees. The intersecting lines create four angles: two acute angles and two obtuse angles. In a coordinate plane, if the slopes of two lines are negative reciprocals of each other, then the lines are perpendicular.

To better understand perpendicular lines, let’s consider an example:

Suppose we have two lines with equations:

Line 1: y = 2x + 3
Line 2: y = -1/2x + 7

To determine if these lines are perpendicular, we can compare their slopes. The slope-intercept form of a line is y = mx + b, where m represents the slope.

The slope of Line 1 is 2, and the slope of Line 2 is -1/2. To check if they are perpendicular, we need to see if their slopes are negative reciprocals of each other.

The negative reciprocal of 2 is -1/2. Therefore, the slopes of these lines are negative reciprocals, indicating that the lines are indeed perpendicular.

Another way to determine if two lines are perpendicular is to use the concept of slope. If the product of the slopes of two lines equals -1, then they are perpendicular. In our example, (2) × (-1/2) equals -1, confirming that the lines are perpendicular.

Visually, perpendicular lines form a right angle, such as the letter “L.” It’s important to note that perpendicular lines have opposite reciprocal slopes, meaning that if one line has slope m, the perpendicular line will have slope -1/m.

In real life, perpendicular lines are commonly found in various applications. For instance, the edges of a rectangular doorframe or window frame form perpendicular lines. The four corners of a square, where the sides intersect at right angles, also represent perpendicular lines.

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