perpendicular lines
Perpendicular lines are two lines that intersect each other at a right angle (90 degrees)
Perpendicular lines are two lines that intersect each other at a right angle (90 degrees). This means that the slopes of the two lines are negative reciprocals of each other.
To understand perpendicular lines, it’s important to understand the concept of slope. The slope of a line measures its steepness and can be calculated using the formula:
slope (m) = (change in y-coordinates) / (change in x-coordinates)
For example, if the coordinates of two points on a line are (x1, y1) and (x2, y2), the slope of the line passing through these points is given by:
slope (m) = (y2 – y1) / (x2 – x1)
Now, for two lines to be perpendicular, their slopes must satisfy the condition that their product is equal to -1. In other words, if the slopes of two lines are m1 and m2, then:
m1 * m2 = -1
This means that if one line has a slope of 2/3, the perpendicular line will have a slope of -3/2.
Visually, perpendicular lines form right angles when they intersect. You can also think of perpendicular lines as being “opposite and reciprocal” in terms of their slopes.
For example, consider two lines with slopes m1 = 2 and m2 = -1/2. Since 2 * (-1/2) = -1, these lines are perpendicular.
In geometry and everyday applications, perpendicular lines are commonly seen in various contexts. For instance, the corners of a square or a rectangle have perpendicular sides, and the lines on a ruler intersect perpendicularly.
Understanding perpendicular lines is crucial in several areas of mathematics, such as geometry, trigonometry, and calculus, as it plays a significant role in solving problems and proving theorems.
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