Perpendicular lines

Perpendicular lines

Introduction

• Perpendicular lines are a fundamental concept in algebra and geometry.
• Two lines are perpendicular if they intersect at a right angle (90 degrees).

Concepts to Understand

• Any two lines are either parallel, intersecting or perpendicular.
• Perpendicular lines can occur in any orientation, i.e., vertically, horizontally or diagonally.
• Perpendicular lines have slopes that are negative reciprocals of each other.

Slope of Perpendicular Lines

• The slope of a line is a measure of its inclination with the horizontal axis.
• If the slopes of two lines are m1 and m2 respectively, and if these lines are perpendicular, it must be true that m1*m2 = -1.
• This is to say, if the slope of one line is m, the slope of the line perpendicular to it will be -1/m.

Calculating Slope

• The slope of a line can be found using the following formula: m = (y2 - y1) / (x2 - x1).
• Here, (x1,y1) and (x2,y2) are any two points on the line.

Equation of a Perpendicular Line

• To find the equation of the line perpendicular to a given line, and passing through a particular point, first find the slope of the given line.
• Reciprocate and negate this slope to get the slope of the perpendicular line.
• Substitute this slope and the coordinates of the given point into the formula for the equation of a line y = mx + c, where m is the slope and c is the y-intercept to obtain the required equation.

Real Life Examples

• Perpendicular lines are present everywhere in daily life, for example, the corners of a book, a football pitch and the cross roads.

Conclusion

• Understanding perpendicular lines, their properties and how to calculate them are key skills in the areas of algebra and geometry.
• Regular practice and applying these concepts to real-life situations can help to solidify understanding.