In the rectangular coordinate system, if line l is parallel to one of the axes, does line contain the point (4, 5)?

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In the rectangular coordinate system, if line l is parallel to one of the axes, does line contain the point (4, 5) ?

(1) Line l contains the point (4, -5).
(2) Line l crosses the x-axis.



OA C

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BTGmoderatorDC wrote:
Tue Nov 23, 2021 6:44 pm
In the rectangular coordinate system, if line l is parallel to one of the axes, does line contain the point (4, 5) ?

(1) Line l contains the point (4, -5).
(2) Line l crosses the x-axis.



OA C

Source: e-GMAT
(1) Line \(l\) contains the point \((4, -5).\)

Then, there are \(2\) possibilities
i) line is parallel to \(y\)-axis
ii) line is parallel to \(x\)-axis

So, no sufficient. \(\Large{\color{red}\chi}\)

(2) Line \(l\) crosses the \(x\)-axis.

That means the line is parallel to \(y\)-axis, but we cannot say if the line \(l\) contains point \((4,5)\)
So, not sufficient. \(\Large{\color{red}\chi}\)

By combining both, we can say line \(l\) contains point \((4,5).\) \(\Large{\color{green}\checkmark}\)

Therefore, C