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In the xy-plane, line l and line k intersect at the point

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In the xy-plane, line l and line k intersect at the point  [#permalink]

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New post 05 Jan 2010, 08:00
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In the xy-plane, line l and line k intersect at the point (16/5, 12/5). What is the slope of line l?

(1) The product of the slopes of line l and line k is –1.
(2) Line k passes through the origin.
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Re: Slope of Line  [#permalink]

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New post 26 Sep 2010, 12:19
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udaymathapati wrote:
In the xy-plane, line l and line k intersect at the point (16/5, 12/5). What is the slope of line l?
(1) The product of the slopes of line l and line k is –1.
(2) Line k passes through the origin.



Line \(l\) passes through the point (16/5, 12/5). If we knew some other point through which line \(l\) passes then we would be able to calculate the slope: the slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line.

(1) The product of the slopes of line \(l\) and line \(k\) is -1 --> line \(l\) and \(k\) are perpendicular to each other (the two lines are perpendicular if and only the product of their slopes is -1). Not, sufficient, as we can have infinite # of perpendicular lines passing through some point (16/5, 12/5).

(2) Line \(k\) passes through the origin --> we have the second point for line \(k\), so we can calculate the slope of \(k\), but we don't know the relationship between the lines \(l\) and \(k\). Not sufficient.

(1)+(2) We can calculate the slope of \(k\) and we know that the product of the slopes of \(l\) and \(k\) is -1, so we can calculate the slope of line \(l\) too. Sufficient.

Answer: C.

For more on these issues check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.
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Re: In the xy-plane, line l and line k intersect at the point  [#permalink]

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New post 05 Jan 2010, 08:14
C..
si) gives us the relation in two lines ..the two r perpendicular to each other...not suff
sii) it gives us the 2nd pt on line k... we can find the slope of k from it but not l.. not suff.
combined frm k ,slope of l can be found frm reln in si..suff
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In the xy-plane, line l and line k intersect at the point  [#permalink]

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New post 26 Sep 2010, 11:49
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In the xy-plane, line l and line k intersect at the point (16/5, 12/5). What is the slope of line l?

(1) The product of the slopes of line l and line k is –1.
(2) Line k passes through the origin.
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Re: Slope of Line  [#permalink]

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New post 26 Sep 2010, 12:22
We know one point in the coordinate system.

(1) Insufficient. First, you must know that perpendicular lines have negative reciprocal slopes. We know that the product of the slopes of l and k is -1, therefore they are perpendicular.

(2) Insufficient. We can now solve for the slope of k, but we know nothing about l.

(1+2) Sufficient, Since we know the slope of k, then we know the slope of l is -1/k.
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Re: Slope of Line  [#permalink]

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New post 26 Sep 2010, 12:24
Bunuel, you are too quick!
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Re: Slope of Line  [#permalink]

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New post 14 Oct 2010, 19:34
C

1) says l and k have opposite slopes. so given point is perpendicular point on intersection ==> NOT SUFF though to find the slope

2) point of intersection and origin will give us the slope of k ==> NOT SUFF by itself since we would not know about the perpendicular bisection

1 + 2 ==> -1/slope of k == slope of l ==> SUFF
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Re: In the xy-plane, line l and line k intersect at the point  [#permalink]

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New post 04 Oct 2016, 22:50
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Let equation of line l --> \(y = Lx + a\)
Let equation of line K --> \(y = Kx + b\)

Both line passes through (16/5, 12/5)

\(16L+5a = 12\) --Eq 1
\(16K+5b = 12\) --Eq2

(1) The product of the slopes of line l and line k is –1.

\(L * K=-1\) --Eq3

We have 3 equation and 4 unknown (a,b,L, M). -- Not sufficient

(2) Line k passes through the origin.

\(b = 0\)
\(16K+5b = 12\) ==> \(16K= 12\) ==> \(\frac{3}{4}\) -- Not sufficient


When we combine (1) and (2), L = -\(\frac{4}{3}\) --Sufficient.

Ans C.
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Re: In the xy-plane, line l and line k intersect at the point  [#permalink]

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Re: In the xy-plane, line l and line k intersect at the point   [#permalink] 21 Oct 2019, 03:27
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