Understanding Perpendicular Lines: How to Identify and Determine Their Relationship

perpendicular

In geometry, perpendicular refers to two lines or line segments that intersect at a right angle (90 degrees)

In geometry, perpendicular refers to two lines or line segments that intersect at a right angle (90 degrees). When two lines are perpendicular, they form four right angles at their intersection point.

To determine if two lines or line segments are perpendicular, we can use the slope of each line. If the product of the slopes of the two lines is -1, then they are perpendicular to each other.

For example, let’s say we have two lines with slopes m1 and m2. If m1 * m2 = -1, then the lines are perpendicular.

To illustrate this, let’s say we have a line with slope m1 = 2. The slope of the perpendicular line, m2, can be found by taking the negative reciprocal of m1. So, m2 = -1/2.

Another way to determine if two lines are perpendicular is by comparing the coefficients of x and y in their respective equations. If the coefficients are negative reciprocals, then the lines are perpendicular.

For instance, if we have two lines given by their equations as:

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

We can observe that the coefficient of x in Line 1 is 2, while in Line 2 it is -1/2. The coefficient of y in Line 1 is 1, while in Line 2 it is -1/2. As the coefficients are negative reciprocals of each other, we can conclude that Line 1 and Line 2 are perpendicular.

In summary, to determine if two lines or line segments are perpendicular, we can:

1. Calculate the slopes of the lines and check if their product is -1.
2. Compare the coefficients of x and y in the equations of the lines and see if they are negative reciprocals of each other.

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