What are Perpendicular Lines What are Perpendicular Lines A line is a basic shape in Geometry. It is an open - ended figure, which is defined to be a collection of points going endlessly in both directions. It is a one - dimensional form with only length as its attribute (i.e. the breadth and height of a line are zero). A pair of lines is used to describe many properties in mathematical discipline. One of the important theories is related to the perpendicular lines. Let us understand that What are Perpendicular Lines. Perpendicular lines the lines that intersect each other at 90 degrees (i.e. at right angles). Take the example of two perpendicular lines L1 and L2. The symbol used to represent lines intersecting at right angles is âŠĽ. Thus, we write: L1 âŠĽ L2 It is interpreted as: L1 is perpendicular to L2.
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One more expression applied for the perpendicular lines is 'normal'. Hence, it can be said that line L1 is normal to line L2. Notice that two perpendicular lines crisscross and create four right angles. In coordinate geometry, the slopes of two perpendicular lines have a definite relationship. Bear in mind that the slope of a line is the tangent of the angle it forms with the abscissa or the x- axis. In a pair of perpendicular lines, if the slope of first line is ‘s1’ then the slope of the second line is given as the negative reciprocal of ‘s1’, or we can write the second line’s slope ‘s2’ mathematically as - 1 / s 1. Thus, s 1 * s 2 = - 1. Example: Two lines ‘K’ and ‘M’ are perpendicular to each other. If the slope of the line ‘K’ is 1, find the slope of line ‘M’? Solution: Let the slope of line ‘K’ is ‘s1’ the slope of line ‘M’ be ‘s2’. Then by the formula s 1 * s 2 = - 1, we can write, - 1 * s 2 = - 1, => s 2 = - 1 / - 1 = 1, Thus, slope of line ‘M’ is equivalent to 1. Example: Consider two lines ‘K’ and ‘M’. If the slope of the line ‘K’ is – 2 and the slope of line ‘M’ is 0.5. Find if the lines ‘K’ and ‘M’ are perpendicular to each other? Solution: Let the slope of line K be s1 the slope of line M be s2. Then to check if the lines are perpendicular to each other, put the values in the formula s1 * s 2 = - 1 and verify if right hand side is equal to the left hand side. Consequently, we can write, Learn More Math Fractions Math.Tutorvista.com
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- 2 * 0.5= - 1.0, Thus, - 2 * 0.5 = - 1, => s 1 * s 2 = - 1, Thus, the lines ‘K’ and ‘M’ are perpendicular to each other. If we characterize two linear functions: k1 = a1 l + b1and k2 = a2 l + b2, and if a1 *a2 = − 1, the graph of the two linear functions will be perpendicular (i.e. at right angles) and will create four right angles where the two lines k1 = a1 l + b1and k2 = a2 l + b2 will intersect.
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Perpendicular lines the lines that intersect each other at 90 degrees (i.e. at right angles). Take the example of two perpendicular lines L1...