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

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by Max@Math Revolution » Mon Sep 03, 2018 3:20 am
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[Math Revolution GMAT math practice question]

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

A. y=-2x
B. y=x/2
C. y=2x
D. y=-x/2
E. y=x
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Which of the following lines is perpendicular to y=(1/2)x?

by fskilnik@GMATH » Mon Sep 03, 2018 5:36 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

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

A. y=-2x
B. y=x/2
C. y=2x
D. y=-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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Max@Math Revolution » Wed Sep 05, 2018 12:58 am
=>

Two lines are perpendicular if and only if the product of their slopes is -1.
Since (1/2)*(-2) = -1, the slope of the line perpendicular to y = (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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