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In triangle ABC with coordinate A(3,4), B(-5,2) and C(1,4) , line segment CF is the altitude of triangle ABC. Determine the equation of the line that collinear to line CF

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the slope of AB is 1/4

So, you want a line with slope -4 that contains C(1,4).

Use the point-slope form, and you have

y-4 = -4(x-1)

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