In the \(xy\)-plane, which of the following two points lie on the line segment that is perpendicular to the line

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C

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In the \(xy\)-plane, which of the following two points lie on the line segment that is perpendicular to the line \(2y = 3x + 6?\)

A. \((-2,4)\) and \((0,1)\)
B. \((5,6)\) and \((6,5)\)
C. \((-4,7)\) and \((-7,9)\)
D. \((1,6)\) and \((-2,4)\)
E. \((-8,12)\) and \((-10,9)\)

Answer: C

Source: e-GMAT