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Geometry

by prachi18oct » Thu Jul 09, 2015 11:00 am
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
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by [email protected] » Thu Jul 09, 2015 3:02 pm
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

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by prachi18oct » Thu Jul 09, 2015 7:14 pm
[email protected] wrote: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

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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 ?
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by Jim@StratusPrep » Fri Jul 10, 2015 4:53 am
Yes. The intercept is the exact point on the coordinate plane. (0, 2) and (0, -2) are different y-intercepts
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by [email protected] » Fri Jul 10, 2015 9:30 am
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.

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