Understanding Perpendicular Lines: Slope Criteria and More

Perpendicular

When two lines are perpendicular to each other, it means that they intersect at a right angle, forming a 90-degree angle

When two lines are perpendicular to each other, it means that they intersect at a right angle, forming a 90-degree angle.

To determine if two lines are perpendicular, you can look at their slopes. The slope of a line is a measure of how steeply it rises or falls as it moves horizontally.

Let’s say we have two lines, Line 1 and Line 2. If the slope of Line 1 is m1 and the slope of Line 2 is m2, then Line 1 and Line 2 are perpendicular if their slopes satisfy the following relationship:

m1 * m2 = -1

In other words, if the product of the slopes is negative one, the lines are perpendicular.

For example, let’s consider a line with a slope of 2. We want to find a line that is perpendicular to it. We can start by setting up the equation:

2 * m2 = -1

To solve for m2, we divide both sides of the equation by 2:

m2 = -1/2

So, a line with a slope of -1/2 would be perpendicular to a line with a slope of 2.

It’s important to note that perpendicular lines have negative reciprocal slopes. That means if one line has a slope of m, the perpendicular line will have a slope of -1/m.

In addition to the slope criteria, there are other ways to determine if two lines are perpendicular, such as using the angle between them. If the angle formed between two lines is 90 degrees, then they are perpendicular.

Remember, lines that are perpendicular to each other intersect at a right angle and have slopes that are negative reciprocals of each other.

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