Find the equation of the line perpendicular to $y = 2x + 3$ and passing through $(4, 1)$.
A$2x + y - 9 = 0$
B$x - 2y - 2 = 0$
C$x + 2y - 6 = 0$CORRECT
D$2x - y - 7 = 0$
JUPEBMathematicsCoordinate Geometry
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Why the answer is C, and why the others tempt you.
A line perpendicular to one with gradient $2$ has gradient $-\dfrac{1}{2}$. Then $y - 1 = -\dfrac{1}{2}(x - 4)$, so $2y - 2 = -x + 4$ and $x + 2y - 6 = 0$. The equation $2x - y - 7 = 0$ is the parallel line through the point, and the others have the wrong sign of gradient.
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