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Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis

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Retired Moderator
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Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis [#permalink]

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New post 12 May 2015, 10:51
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

60% (00:57) correct 40% (01:27) wrong based on 192 sessions

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Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis?

A. 0
B. 1/(√3)
C. 1
D. √3
E. 5
[Reveal] Spoiler: OA

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Re: Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis [#permalink]

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New post 12 May 2015, 21:21
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Hi reto,

The question gives us two line segments and asks us the height of the intersection point of these line segments from the x- axis i.e. we need to find the y coordinate of the intersection point of the line segments.

We need to solve the equations of the line segments to find out the value of \(y\)

\(y=√3x−2\) ..... (1)

\(y=2√3x−5\)..... (2)

Multiplying equation (1) by 2 and subtracting equation (2) from equation (1) would give us

\(y = 1\)

Hence the answer is Option C

Hope it helps!

Regards
Harsh
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Re: Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis [#permalink]

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New post 07 Oct 2015, 02:35
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Just solve two equations for y:
y=sqrt3*x-2
y=2sqrt3*x-5

x=(y+2)/sqrt3

substitute for x

2sqrt3*(y+2/sqrt3)-5
y=2y+4-5
y=1

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Re: Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis [#permalink]

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New post 17 Feb 2017, 17:23
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Re: Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis [#permalink]

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New post 17 Feb 2017, 18:49
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reto wrote:
Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis?

A. 0
B. 1/(√3)
C. 1
D. √3
E. 5



Hi..

Most important point..
you can easily find value of x and y as two equations and two variables..
BUT height from x axis will be value of y and not value of x..


y=√3·x−2 and y=2√3·x−5 ...
So y=√3·x−2 =2√3·x−5 .......√3·x=3......X=√3

So y =√3*x-2=√3*√3-2=3-2=1

C
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Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis [#permalink]

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New post 19 Feb 2017, 08:59
Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis?

A. 0
B. 1/(√3)
C. 1
D. √3
E. 5

If same question is ask in term of x-axis should we need to eliminate "y" correct me if I am wrong
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Target#01 Q45,V20--April End

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Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis [#permalink]

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New post 21 May 2017, 17:34
chetan2u wrote:
reto wrote:
Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis?

A. 0
B. 1/(√3)
C. 1
D. √3
E. 5



Hi..

Most important point..
you can easily find value of x and y as two equations and two variables..
BUT height from x axis will be value of y and not value of x..


y=√3·x−2 and y=2√3·x−5 ...
So y=√3·x−2 =2√3·x−5 =>√3·x=3......X=√3

So y =√3*x-2=√3*√3-2=3-2=1

C


Hi Chetan2u ... can you breakdown the highlighted steps above?
Lines y=√3·x−2 and y=2√3·x−5 intersect at what height above the x axis   [#permalink] 21 May 2017, 17:34
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