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The line passing through (3,1) and (0,2) is perpendicular to the line passing through (5,7) and (4,x). What is the value of x?
Slope of line passing through (3,1) and (0,2) = $$\frac{(2 - 1)}{(0 - 3)} = \frac{-1}{3}$$
Slope of line passing through (5,7) and (4,x) = $$\frac{(x - 7)}{(4 - 5)} = -(x - 7)$$
Also, product of slopes of line which are perpendicular to each other = -1
=> $$-(x - 7) \times \frac{-1}{3} = -1$$
=> $$(x - 7) = -3$$
=> $$x = 7 - 3 = 4$$
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