Co-ordinate Geometery

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[email protected]: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Thu Jul 03, 2008 4:52 am

by [email protected] » Sat Aug 02, 2008 8:08 am

Hi

Anyone know how to solve this?

At which point on the coordinate plane do the follwing lines intersect?

y1 = 2x + b

y2 = mx - 1

1) the slope of y1 is the negation of slope y2

2) y1 passes through the origin

Thanks in advance!

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Source: Beat The GMAT — Data Sufficiency | Sat Aug 02, 2008 8:08 am

pepeprepa: Legendary Member; Posts: 661; Joined: Tue Jul 08, 2008 12:58 pm; Location: France; Thanked: 48 times

by pepeprepa » Sat Aug 02, 2008 9:25 am

1)
y1 = 2x + b
y2 = -2x - 1
You do not have b so there is an infinity of solutions (y1 could be all the parallel lines with slope 2).

2)
y1 = 2x
y2 = mx - 1
This time you have y1 but you do not know the slope of y2, you do not know the direction of y2 so that is the same you have an infinity of solutions.

1) and 2)
y1 = 2x
y2 = -2x - 1
You have the equations of the two lines y1 and y2 so it is ok you know where they intersect.

That is C, you need both.

-----

If you want to find it
2x=-2x-1
4x=-1
x=(-1/4)

And for the y you put x=(-1/4) in the equation of y1 or y2 that is the same result given they intersect at this point:
2*(-1/4)=-1/2
-2*(-1/4)-1=-1/2

They intersect at (-1/4;-1/2)

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