Understanding Perpendicular Lines: How to Determine Perpendicularity and Calculate Slopes

Perpendicular Lines

Perpendicular lines are a fundamental concept in geometry

Perpendicular lines are a fundamental concept in geometry. Two lines are said to be perpendicular to each other if they intersect at a right angle, which means that their angle of intersection is 90 degrees (or π/2 radians).

To determine if two lines are perpendicular, you can check the slope of each line. The slope of a line is represented by the letter “m” and is calculated by dividing the difference in y-coordinates by the difference in x-coordinates between any two points on the line. If the product of the slopes of two lines is -1, then they are perpendicular to each other.

For example, let’s consider the equations of two lines: y = 3x + 2 and y = -1/3x + 4. To determine if these lines are perpendicular, we first need to find their slopes.

The slope of the first line, y = 3x + 2, is 3. This can be seen because the coefficient of x is 3 in the equation. So, the slope of the first line is m₁ = 3.

The slope of the second line, y = -1/3x + 4, is -1/3. Similarly, the coefficient of x is -1/3 in the equation. Thus, the slope of the second line is m₂ = -1/3.

Now, we can calculate the product of the slopes: m₁ * m₂ = 3 * (-1/3) = -1.

Since the product of the slopes is -1, we can conclude that the two lines y = 3x + 2 and y = -1/3x + 4 are perpendicular to each other.

It’s important to note that the concept of perpendicular lines extends beyond just straight lines. In three-dimensional space, perpendicularity exists between planes and line segments as well. In higher dimensions, the notion of perpendicularity is generalized further.

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