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Definition of Perpendicular Lines Two intersecting lines will have four angles formed at the intersection points. If all the four angles are equal, then the two lines are said to be perpendicular to each other. We already know by linear postulate theorem that the two vertically opposite angles are equal. Hence if these two lines are perpendicular, then all four angles are 90 degrees. Examples of perpendicular lines: In the graph paper, The X-axis and Y-axis are perpendicular. In an ellipse two axes, minor axis, and major axis are perpendicular. For a line segment, any shortest line from a point outside the circle is perpendicular. Tangent and normal to any curve are perpendicular lines. Slopes of two perpendicular lines: In coordinate Geometry, when two lines are perpendicular, the product of the slopes of the lines is -1. This property has a lot of applications in finding the equation of perpendicular lines, length of perpendicular segment from a point to a given line, etc. Know More About Online Tutors For Free


For any curve in a graph with equation y = f(x), the slope of the tangent is defined as the rate of change of y with respect to x at that point. The normal to this curve at this point is perpendicular to the tangent line. Example: In a circle, with centre at the origin and radius 3, the equation will be of the form (x)²+(y)² = 3². Take any point say (0,3). To find the tangent, we have to find dy/dx. Differentiating, 2x+2y =0 Hence, the slope of the normal is perpendicular to x axis or parallel to y axis. Example for Perpendicular Lines from a Point to a Line Let AB be a line with coordinates (1,2) and (3,4). Measure the length of perpendicular line from (-1,1) to this line segment. We know that the perpendicular line from (-1,1) has a slope of -1/slope of AB. Equation of AB is (x-1)/(3-1) = (y-2)/(4-2) Or x-1 = y-2 Or y = x+1 Slope of AB passing through (1,2) and (3,4) is 4 - 2/3 -1 =1. Slope of perpendicular line to AB is -1. Learn More Free Math Tutor Online Chat


Since the perpendicular line passes through (-1,1) equation of the perpendicular is y-1 = -1(x+1) or y =-x -1 +1 or y = -x. To get the foot of the perpendicular line on AB, we solve the two equations by substitution method. y = x+1 = -x This on simplification gives 2x = -1 or x = -1/2. Since y = -x , we have y = +1/2, So, foot of the altitude from the point (-1,1) is (-1/2,1/2). The length of the perpendicular segment is between (-1,1) and (-1/2,1/2) is √[ (-1/2+1)²+(1/2-1)²] = √(1/4+1/4) = √(1/2) = 1/1.414 = 0.707 approximately. Length of the Perpendicular Line Perpendicular Line is when two lines intersect to form a 90 degree angle. To find the Length of the Perpendicular line, explanation is given below


Equation of Line In geometry, a line is a straight curve. Lines are used to represent straight objects with negligible width and height. A line segment is a part of a given line that is bounded by two distinct end points and contains every point on the line between its end points. A line has a zero curvature and it has no thickness. It has no ends and so it extends indefinitely. Different Types of Lines Lines are classified in to different types based on their properties. The different types of lines are, --Straight Line --Vertical line --Horizontal line


--Skew Lines --Parallel Lines --Perpendicular Lines --Transversal Lines Equation of a Line General form: A straight line is defined by a linear equation whose general form is, Ax+By+C=0, Where A, B are not both 0. Slope- intercept equation: The equation of line with a given slope value m and the y-intercept b is; y=mx+b Read More About Online Free Math Tutoring


Line through two points: The line passing through two distinct points (x1, y1) and (x2, y2) is given by, y = y1 + [(y2 - y1) / (x2 - x1)] 路(x - x1), Where x1 and x2 are assumed to be different. Line Equation (1) can also be written as y - y1 = [(y2 - y1) / (x2 - x1)]路(x - x1)


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Definition of Perpendicular Lines