Carcass wrote:
In the coordinate plane, Line H has a positive slope, and Line J never passes through the first quadrant. Which of the following could be true?
I. line J is perpendicular to line H
II. line J is parallel to line H
III. line J intersects line H on the x-axis
A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITIONGRE - Math Book GIVEN: Line J never passes through the first quadrantThis means
line J has a NEGATIVE slope, AND line J has a negative y-intercept (see below for an example of how line J might look)
I. line J is perpendicular to line H
POSSIBLE (see diagram below)
II. line J is parallel to line H
We know that
line J has a NEGATIVE slope and we're told that line H has a POSITIVE slope.
In order for two lines to be parallel, their slopes must be equal.
Since a NEGATIVE slope can never equal a POSITIVE slope, statement II is NOT possible.
III. line J intersects line H on the x-axis
POSSIBLE (see diagram below)
Answer: C
Cheers,
Brent