Simple rule I'm missing?

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gusterguy

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Nov 23, 2007
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"Line l has a positive slope and passes through the point (0,0). If line k is perpendicular to line l, which of the following must be true?

A - Line k passes through the point (0, 0)
B - Line k has a positive slope
C - Line k has a negative slope
D - Line k has a positive x-intercept
E - Line k has a negative y-intercept

OK, so if two lines are perpendicular to each other - I know their slopes are negative reciprocals of each other. With only one point though how do I find a slope? I know I know all the information to do this problem, for some reason determining what knowledge comes in to play is giving me a hard time.

Any ideas on where I should go from here?
 
gusterguy said:
With only one point though how do I find a slope?
Click to expand...
You're not actually asked to find the slope; you only need to find the option which "must" be true. So work through the list, eliminating options for which you can find counter-examples. :idea:

For instance, option one says that the perpendicular line must pass through the origin. But isn't the original line infintely long, and can't you find infinitely-many perpendicular lines through it? And won't only one of those lines also pass through the origin? So you can cross that option off. :wink:

And so forth, until you're down to only one option left, which must be the right one! :D

Eliz.
 
gusterguy said:
"Line l has a positive slope and passes through the point (0,0). If line k is perpendicular to line l, which of the following must be true?

A - Line k passes through the point (0, 0)
B - Line k has a positive slope
C - Line k has a negative slope
D - Line k has a positive x-intercept
E - Line k has a negative y-intercept

OK, so if two lines are perpendicular to each other - I know their slopes are negative reciprocals of each other. With only one point though how do I find a slope? I know I know all the information to do this problem, for some reason determining what knowledge comes in to play is giving me a hard time.

Any ideas on where I should go from here?
Click to expand...

What is the relationship between the slopes of two lines that are perpendicular to each other?
 
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