Geometry

[prachi18oct]

If the slope of l2 is equal to that of a different line, l1, which of the following could be true?

I. l1 and l2 have the same x-intercept.

II. l1 and l2 have the same y-intercept.

III. l1 and l2 have exactly 1 point in common.

A None
B II only
C III only
D I and II only
E I, II and III

[[email protected]]

Hi prachi18oct,

Since we're told that the slopes of two DIFFERENT lines are the SAME, then those two lines are PARALLEL and would have NO POINTS in common (try drawing any 2 parallel lines and you'll see). All 3 Roman Numerals ask about whether the two lines have points in common, which is NOT possible under any circumstances. As such, non of them can be true.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

[prachi18oct]

Hi prachi18oct,

Since we're told that the slopes of two DIFFERENT lines are the SAME, then those two lines are PARALLEL and would have NO POINTS in common (try drawing any 2 parallel lines and you'll see). All 3 Roman Numerals ask about whether the two lines have points in common, which is NOT possible under any circumstances. As such, non of them can be true.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

I thought the x- intercept or y intercept is an absolute value and so either of the two can be equal for two parallel lines.So it is not true then. When we say x-intercept it is the exact point on x axis where the line intersects and is not measured as the absolute distance from origin ?

[Jim@StratusPrep]

Yes. The intercept is the exact point on the coordinate plane. (0, 2) and (0, -2) are different y-intercepts

[[email protected]]

Hi prachi18oct,

By definition, the X-intercept and Y-intercept of a line are the exact points where the line crosses the X-axis and Y-axis, respectively. In my earlier post, I suggested that you draw two parallel lines so that you could "see" them and how they compare - that still serves as an easy way to prove the concept. When dealing with parallel lines, NO points are common.

GMAT assassins aren't born, they're made,
Rich