  Question

(i) Is the line 3x + 4y + 7 = 0 perpendicular to the line 28x - 21y + 50 = 0 ? (ii) Is the line x - 3y = 4 perpendicular to the line 3x - y = 7 ? (iii) Is the line 3x + 2y = 5 parallel to the line x + 2y = 1 ? (iv) Determine x so that the slope of the line through (1, 4) and (x, 2) is 2.

Solution

(i) 3x + 4y + 7 = 0 Slope of this line = 28x - 21y + 50 = 0 Slope of this line = Since, product of slopes of the two lines = -1, the lines are perpendicular to each other. (ii) x - 3y = 4 3y = x - 4 y = Slope of this line = 3x - y = 7 y = 3x - 7 Slope of this line = 3 Product of slopes of the two lines = 1 -1 So, the lines are not perpendicular to each other. (iii) 3x + 2y = 5 2y = -3x + 5 y = Slope of this line = x + 2y = 1 2y = -x + 1 y = Slope of this line = Product of slopes of the two lines = 3 -1 So, the lines are not perpendicular to each other. (iv) Given, the slope of the line through (1, 4) and (x, 2) is 2. MathematicsConcise MathematicsStandard X

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