In the xy-plane, which of the following two points lie on the line segment that is perpendicular to the line 2y =

[BTGmoderatorDC]

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)



OA C

Source: e-GMAT

[swerve]

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)



OA C

Source: e-GMAT

To lie on the line segment that is perpendicular to \(2y = 3x + 6 \Rightarrow y = \dfrac{3}{2}x + 3\).

Slope of that line segment should be perpendicular to \(\dfrac{3}{2}\)

\(m_1 \cdot m_2 = -1 \quad \Rightarrow \quad m2=-\dfrac{2}{3}\)

So, find the slope of options and check which option gives a slope of \(-\dfrac{2}{3}\)

A. \((-2,4)\) and \((0,1)\). \(m = \dfrac{1 - 4}{0 - (-2)} = -\dfrac{3}{2}\, \Large{\color{red}\chi}\)

B. \((5,6)\) and \((6,5)\). \(m = \dfrac{5 - 6}{6 - 5} = -1\, \Large{\color{red}\chi}\)

C. \((-4,7)\) and \((-7,9)\). \(m = \dfrac{9 - 7}{-7 - (-4)} = \dfrac{2}{-3} = -\dfrac{2}{3}\, \Large{\color{green}\checkmark}\)

Therefore, C