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In the xy-coordinate plane, Line J passes through points (−2,0) and (0

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Joined: 02 Sep 2009
Posts: 50042
In the xy-coordinate plane, Line J passes through points (−2,0) and (0  [#permalink]

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07 Feb 2018, 20:50
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86% (01:36) correct 14% (02:37) wrong based on 84 sessions

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In the xy-coordinate plane, Line J passes through points (−2,0) and (0,2). Line K passes through points (4,0) and (0,4). If point (j,k) is the point at which Line J and Line K intersect, which of the following is true of point (j,k)?

A. j>0 and k>0
B. j>0 and k<0
C. j<0 and k<0
D. j<0 and k>0
E. The product jk=0

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Joined: 27 Dec 2017
Posts: 27
Re: In the xy-coordinate plane, Line J passes through points (−2,0) and (0  [#permalink]

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07 Feb 2018, 20:57
1
As we draw lines in the xy plane, the only quadrant the lines will meet is 1 St quadrant . So j and k should be >o ..A is correct

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Joined: 16 Jan 2018
Posts: 92
Location: New Zealand
Re: In the xy-coordinate plane, Line J passes through points (−2,0) and (0  [#permalink]

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07 Feb 2018, 22:40
Since, line j lies on x-axis, the intersection will also lie on the x-axis and as such, the y-coordinate of the intersection point will be zero.

So, the product of JK will be '0'. Answer is E.

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Joined: 31 May 2017
Posts: 322
Re: In the xy-coordinate plane, Line J passes through points (−2,0) and (0  [#permalink]

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08 Feb 2018, 21:06
When we draw the line J and K using the points given, the line J and K would intersect when both J and K is greater than 0.

Ans: A
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In the xy-coordinate plane, Line J passes through points (−2,0) and (0  [#permalink]

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09 Feb 2018, 09:37
Bunuel wrote:
In the xy-coordinate plane, Line J passes through points (−2,0) and (0,2). Line K passes through points (4,0) and (0,4). If point (j,k) is the point at which Line J and Line K intersect, which of the following is true of point (j,k)?

A. j>0 and k>0
B. j>0 and k<0
C. j<0 and k<0
D. j<0 and k>0
E. The product jk=0

I usually graph, but finding the equations for these lines is quick.

To find the intersection point for two lines: set the equations for y equal; solve for x (x-coordinate = j); then solve for y (y-coordinate = k)

Write the equation of the lines in slope-intercept form.
y = mx + b
m = slope = $$\frac{rise}{run}=\frac{(y_2-y_1)}{(x_2-x_1)}$$
b = y-intercept

Line J has slope $$\frac{(0-2)}{(-2-0)}=\frac{-2}{-2} = 1$$

From the prompt, when x=0, b = 2 (y-intercept)
Line J: y = (1)x + 2

Line K's slope: $$\frac{(4-0)}{(0-4)}=\frac{4}{-4} = -1$$

When x=0, b = 4 (y-intercept)
Line K: y = (-1)x + 4

Set equations for y equal, solve for x
x + 2 = -x + 4
2x = 2
x = 1 (= the x-coordinate of the intersection point, = j)
Plug x in to find y-coordinate:
y = 1 + 2
y = 3 (= y-coordinate of intersection point, k)

Intersection point is (j,k) = (1,3)

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In the xy-coordinate plane, Line J passes through points (−2,0) and (0 &nbs [#permalink] 09 Feb 2018, 09:37
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