Question 83

The line passing through (1,x) and (3,0) is perpendicular to the line passing through (5,1) and (4,4). What is the value of x?

Solution

Slope of the line passing through (1,x) and (3,0) = $$\frac{(0 - x)}{(3 - 1)} = \frac{-x}{2}$$

Slope of the line passing through (5,1) and (4,4) = $$\frac{(4 - 1)}{(4 - 5)} = -3$$

Product of slopes of two perpendicular lines = -1

=> $$(\frac{-x}{2}) \times (-3) = -1$$

=> $$x = \frac{-2}{3}$$

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The line passing through (­1,x) and (3,0) is perpendicular to the line passing through (5,1) and (4,4). What is the value of x?