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Which of the following lines is perpendicular to y=(1/2)x?

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Which of the following lines is perpendicular to y=(1/2)x?  [#permalink]

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New post 03 Sep 2018, 04:22
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A
B
C
D
E

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  15% (low)

Question Stats:

88% (00:14) correct 12% (00:43) wrong based on 26 sessions

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[Math Revolution GMAT math practice question]

Which of the following lines is perpendicular to \(y=(\frac{1}{2})x\)?

\(A. y=-2x\)
\(B. y=\frac{x}{2}\)
\(C. y=2x\)
\(D. y=\frac{-x}{2}\)
\(E. y=x\)

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Re: Which of the following lines is perpendicular to y=(1/2)x?  [#permalink]

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New post 03 Sep 2018, 04:40
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Which of the following lines is perpendicular to \(y=(\frac{1}{2})x\)?

\(A. y=-2x\)
\(B. y=\frac{x}{2}\)
\(C. y=2x\)
\(D. y=\frac{-x}{2}\)
\(E. y=x\)


For one line to be perpendicular to another, the relationship between their slopes has to be negative reciprocal.

Slope of \(y=(\frac{1}{2})x\) is \(= \frac{1}{2}\)

Therefore slope of perpendicular line should be \(= -2\)

\(y = -2x\)

Answer A...
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Re: Which of the following lines is perpendicular to y=(1/2)x?  [#permalink]

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New post 03 Sep 2018, 04:44
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Which of the following lines is perpendicular to \(y=(\frac{1}{2})x\)?

\(A. y=-2x\)
\(B. y=\frac{x}{2}\)
\(C. y=2x\)
\(D. y=\frac{-x}{2}\)
\(E. y=x\)



when two lines are perpendicular the product of their slops = -1
or
m1*m2=-1
m1 = 1/2
m2=-2

point slope form => y=mx+c
y=-2x
A
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Re: Which of the following lines is perpendicular to y=(1/2)x?  [#permalink]

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New post 03 Sep 2018, 04:58
( A ) as product of slopes of 2 perpendicular lines is -1.

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Re: Which of the following lines is perpendicular to y=(1/2)x?  [#permalink]

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New post 03 Sep 2018, 06:41
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Which of the following lines is perpendicular to \(y=(\frac{1}{2})x\)?

\(A. y=-2x\)
\(B. y=\frac{x}{2}\)
\(C. y=2x\)
\(D. y=\frac{-x}{2}\)
\(E. y=x\)


Two lines are perpendicular if, and only if, they satisfy one the two geometric configurations below:

1. One of them is vertical (slope not defined) and the other is horizontal (slope is zero)
2. Both are oblique (i.e., non-horizontal and non-vertical) and, in this case, the product of their slopes must be -1.

The line given in the question stem is oblique, with slope 1/2, therefore we look for a line with slope -2.

Answer: A

The above follows the notations and rationale taught in the GMATH method.
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Re: Which of the following lines is perpendicular to y=(1/2)x?  [#permalink]

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New post 05 Sep 2018, 02:17
=>

Two lines are perpendicular if and only if the product of their slopes is \(-1\).
Since \((\frac{1}{2})*(-2) = -1\), the slope of the line perpendicular to \(y = (\frac{1}{2})x\) is \(-2\).
The only answer choice with a slope of \(-2\) is A.

Therefore, A is the answer.
Answer: A
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Re: Which of the following lines is perpendicular to y=(1/2)x? &nbs [#permalink] 05 Sep 2018, 02:17
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