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Does the point of intersection of line y = kx + b and line x

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Does the point of intersection of line y = kx + b and line x [#permalink]

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New post 15 Mar 2008, 11:52
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Does the point of intersection of line y = kx + b and line x = ky + b have a negative x-coordinate?
1. k > 0, b > 0
2. k > 1

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Re: Ds coordinate geo [#permalink]

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New post 15 Mar 2008, 12:23
C

Solving for x.. x= b(k+1)/(1-k^2)

1: can't tell what sign 1-k^2 is (k could be 0<k<1 or k=1 or k>1)
2: 1-k^2 is negative, but final sign depends on b's sign

combined - denominator is negative and numerator is positive, so x-coordinate must be negative.
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Re: Ds coordinate geo [#permalink]

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New post 15 Mar 2008, 17:14
marcodonzelli wrote:
Does the point of intersection of line y = kx + b and line x = ky + b have a negative x-coordinate?
1. k > 0, b > 0
2. k > 1


Yes; the x-coordinate will be negative.
y= kx + b-------1

y= x/k - b/k-----2

Since the 2 equations have inverse slopes, they must represent perpendicular lines.
Take equation 1 first.
If y= 0, x= -b/k; If x= 0, y= b. Joining these 2 points, one gets a line going from -x-coordinate to +y coordinate. Now, if you plot the 2nd equation similarly, you find that when
x = 0, y = -b/k and when y = 0, x = b. On plotting these points it is seen that the 2 lines will intersect in the 3rd quadrant. Thus, x is negative.
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Re: Ds coordinate geo [#permalink]

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New post Updated on: 22 Sep 2011, 01:42
Two line
y=kx+b ------1
y=x/k - b/k -------2
Subtracting 2 from 1
0=kx + b - (x/k - b/k)
0=kx - x/k + b + b/k
b/k -b = -kx + x/k
b(1/k + 1) = x(1/k - k)
b(1+k)/k = x[1-k^2/k]
b(1+k) = x(1-k^2)
b(1+k) = x(1+k)(1-k)
b = x(1-k)
x= b/(1-k)

1-k does the trick because even if k>0, it can be +ve or -ve thus making x +ve or -ve.

OA C.
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Originally posted by jamifahad on 21 Sep 2011, 05:32.
Last edited by jamifahad on 22 Sep 2011, 01:42, edited 1 time in total.
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Re: Ds coordinate geo [#permalink]

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New post 21 Sep 2011, 23:02
by solving - y= 1/k x -b/k = kx + b

thus x = b/ 1-k

a not sufficient since k > 1 is not known.

b not sufficient since b is not known.

a+b

sufficient, x is negative.

C is it.
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Re: Does the point of intersection of line y = kx + b and line x [#permalink]

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New post 24 Nov 2017, 09:08
marcodonzelli wrote:
Does the point of intersection of line y = kx + b and line x = ky + b have a negative x-coordinate?
1. k > 0, b > 0
2. k > 1


PROPER VERSION OF THIS QUESTION IS DISCUSSED HERE: if-k-does-not-equal-1-0-or-1-does-the-point-of-intersection-of-line-189958.html

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Re: Does the point of intersection of line y = kx + b and line x   [#permalink] 24 Nov 2017, 09:08
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