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In the xy co ordinate plane, line l and line k intersect at

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In the xy co ordinate plane, line l and line k intersect at [#permalink]

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In the xy co ordinate 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 intercepts of line l and k is negative

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Re: DS- Coordinate Geometry ( GMAT_prep) [#permalink]

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New post 12 Jan 2009, 11:09
sandipchowdhury wrote:
In the xy co ordinate 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 intercepts of line l and k is negative

y=m1x+c1
y=m2x+c2
x-intercepts are -c1/m1 and -c2/m2
Further c1=3-4m1 and c2=3-4m2
c1c2 = 9-4(m1+m2)+16m1m2
c1c2/m1/m2 = 9/m1/m2-4(1/m1+1/m2)+16

Both statements are not sufficient. because m1+m2 will be unknown. Simpler way is by using graphs; nonetheless not sufficient.
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tusharvk

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Re: DS- Coordinate Geometry ( GMAT_prep) [#permalink]

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New post 13 Jan 2009, 14:32
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The OA is C.

line L: y1 = m1x1 + b1; x-intercept = -b1/m1; y-intercept = b1
line K: y2 = m2x2 + b2; x-intercept = -b2/m2; y-intercept = b2

(4,3) lies on both.
3 = 4m1 + b1 = 4m2 + b2

Is m1m2 < 0?

1. (-b1/m1)*(-b2/m2) > 0
b1b2/m1m2 > 0
If b1b2 > 0, m1m2 > 0
If b1b2 < 0, m1m2 < 0
NOT SUFFICIENT.

2. b1b2 < 0
(3-4m1)(3-4m2) < 0
NOT SUFFICIENT.

Together, b1b2 < 0 and m1m2 < 0.
SUFFICIENT. Answer is C.

Another way to solve this:

1. X1*X2 > 0

means both lines could have -ve x-intercepts or +ve x-intercepts

cond 1:
if both lines have -ve x-intercepts they have +ve slopes as they pass thru point (4,3) so m1m2>0

cond 2:
if both lines have +ve x-intercepts.

the line(s) could go from left to right passing thru (4,3) which means +ve slope
the line(s) could go from right to left passing thru (4,3) which means -ve slope

We cannot be sure how Lines L and K intercept X axis - INSUFFICIENT

2. Y1*Y2 < 0

means Y1 < 0 OR Y2 < 0

if Y1< 0 line has pass thru (4,3) = +ve slope
other line can be pass from down up or bottom down thru (4,3) so slope is unknown INSUFFICIENT

TOGETHER one line passes down up and other bottom down for both conditions to be true and hence SUFFICIENT

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Re: DS- Coordinate Geometry ( GMAT_prep)   [#permalink] 13 Jan 2009, 14:32
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In the xy co ordinate plane, line l and line k intersect at

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