Definition of Perpendicular Lines

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We can define perpendicular lines are lines, which have angle between them are right angle (90O). In other words we can say perpendicular lines are lines, having product of slopes -1. Means if the slope of a line is 2, then the slope of perpendicular line is – (1/2). If we have line ax + by + c = 0, we know the equation of perpendicular line bx – ay + k = 0.

Problem 1: If we have a equation of a line 3x - 4y + 7 =0, find the equation of a line which is perpendicular to the given line and passes through (1, 0).

Solution: Step1: The equation of given line is 3x – 4y + 7 = 0

=> Step2: The line perpendicular to 3x – 4y + 7 = 0 is 4x + 3y + k =0

=> Step3: We know, this line passes through (1, 0), so we need to plug the values in this equation to get the value of k
=> 4 (1) + 3 (0) + k = 0
=> k = - 4

=> Step 4: The required equation of a line is 4x + 3y – 4 =0.
 


Problem 2: If we have an equation of a line 2x + 3y + 4 =0, find the equation of a line which is perpendicular to the given line and passes through (1, 1).

Solution: Step1: The equation of given line is 2x + 3y + 4 = 0

=> Step2: The line perpendicular to 2x+ 3y + 4 = 0 is 3x – 2y + k =0

=> Step3: We know, this line passes through (1, 1), so we need to plug the values in this equation to get the value of k
=> 3 (1) – 2 (1) + k = 0
=> k =- 1

=> Step 4: The required equation of a line is 3x – 2y - 1 =0.

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