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corrdinate geometry slope problem

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Intern
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corrdinate geometry slope problem [#permalink]

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New post 13 Jun 2009, 15:14
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Hi guys was wondering if anyone could offer a method to solve this problem:

In the xy coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative?

(1) The product of the X-intercepts of line L and K is positive.

(2) The product of the y-intersepts of lines L and K is negative.

Answer: C.

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Re: corrdinate geometry slope problem [#permalink]

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New post 14 Jun 2009, 05:21
This is what I got.

Attachment:
Geo.gif
Geo.gif [ 11.74 KiB | Viewed 1101 times ]

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Re: corrdinate geometry slope problem [#permalink]

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New post 16 Jun 2009, 01:22
In the xy coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative?

(1) The product of the X-intercepts of line L and K is positive.

There is another way to draw the graph.

When lines K and L both have negative x-intercepts, they both can have positive slopes and intersecting y-axis at positive values, and then meet at (4,3). Since we do not know whether the graph looks like yours (negative product) or mine (positive product), (1) is NOT SUFFICIENT.


(2) The product of the y-intercepts of lines L and K is negative.

It is for sure that one of the lines will be at negative y-intercept while the other at the positive end.

Referring the graph you have drawn, we can draw line K to be +ve slope by lowering the y-intercept or -ve slope by increasing the y-intercept. The product of their slopes again can be either +ve or -ve. Hence (2) is also NOT SUFFICIENT.


(1) + (2)

In the statement 1 explanation, I introduced another way of drawing the graph. Note that both lines are of positive slopes. However, putting (2) into the picture, my graph is no longer valid. Since your graph is the only solution that fits both statements, C is the correct answer.

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Re: corrdinate geometry slope problem [#permalink]

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New post 16 Jun 2009, 02:00
y1 = m1x1 + b1 and y2 = m2x2 + b2

X intrecepts are (-c1/m1) and (-c2/m2)
y intercepts are c1,c2

it passes througth the pont (4,3)

Stmt 1 :

c1c2 / m1m2 > 0 . c1c2 and m1m2 >0 or c1c2 <0 and m1m2 <0

So Insufficient.

Stmt 2 :

c1.c2 < 0 . Insufficient.

combining

c1.c2 < 0 and c1c2 / m1m2 > 0 . then m1m2 needs to be < 0.

Hence C.

What puzzeles me is that the information the Line passes to ( 4,3) i have not used it self. Is my explaination correct?

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Re: corrdinate geometry slope problem   [#permalink] 16 Jun 2009, 02:00
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