filipembribeiro wrote:
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.
I am uploading a graph for anyone who needs clarification on why
the answer is (C).
Attachment:
Screen Shot 2021-02-12 at 10.36.09.png [ 20.07 KiB | Viewed 2905 times ]
Statement (1) tells us that (4, -5) is on the graph of the line, but looking at the image above, we cannot tell whether that point exists on the
red line, in which case the answer to the question would be yes, or on the
green line, which would make the answer to the question no. Since both lines conform to the given information about line l being parallel to one of the axes, we cannot say that statement (1) is sufficient on its own.
Statement (2) is even more open-ended, with an infinite number of vertical lines possible in the image above. Of course, one of these, the
red line, would lead to a yes answer, but any other line would lead to a no answer. Hence, statement (2) is not sufficient on its own.
Taken together, there is no way the line can be parallel to the x-axis, as the
blue line shows, since it would not contain the point (4, -5) from statement (1) and would not cross the x-axis, per statement (2). The only valid line, the one that conforms to both statements, is the
red line, and the answer to the question is yes, but only if both statements are taken together: (C).
I hope that helps if anyone was confused. Good luck with your studies.
- Andrew
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