Definition of Perpendicular Lines

Definition of Perpendicular Lines 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.