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# If line l is perpendicular to line k, which of the following must be

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Math Expert
Joined: 02 Sep 2009
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If line l is perpendicular to line k, which of the following must be  [#permalink]

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17 Jan 2019, 03:02
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97% (00:23) correct 3% (01:03) wrong based on 42 sessions

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If line l is perpendicular to line k, which of the following must be true?

A. The slopes of l and k are equal.

B. The product of the slopes of l and k is 1.

C. The product of the slopes of l and k is −1.

D. The y-intercepts l and k are equal.

E. The x-intercepts of l and k are equal.

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Re: If line l is perpendicular to line k, which of the following must be  [#permalink]

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17 Jan 2019, 03:15
Bunuel wrote:
If line l is perpendicular to line k, which of the following must be true?

A. The slopes of l and k are equal.

B. The product of the slopes of l and k is 1.

C. The product of the slopes of l and k is −1.

D. The y-intercepts l and k are equal.

E. The x-intercepts of l and k are equal.

For one line to be perpendicular to another, the relationship between their slopes has to be negative reciprocal −1/m. In other words, the two lines are perpendicular if and only if the product of their slopes is −1.

Hence C
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Re: If line l is perpendicular to line k, which of the following must be  [#permalink]

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17 Jan 2019, 07:32
Bunuel wrote:
If line l is perpendicular to line k, which of the following must be true?

A. The slopes of l and k are equal.

B. The product of the slopes of l and k is 1.

C. The product of the slopes of l and k is −1.

D. The y-intercepts l and k are equal.

E. The x-intercepts of l and k are equal.

The product of the slopes of l and k is −1.

this would be true always for perpendicular lines
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Re: If line l is perpendicular to line k, which of the following must be  [#permalink]

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21 Jan 2019, 19:06
Bunuel wrote:
If line l is perpendicular to line k, which of the following must be true?

A. The slopes of l and k are equal.

B. The product of the slopes of l and k is 1.

C. The product of the slopes of l and k is −1.

D. The y-intercepts l and k are equal.

E. The x-intercepts of l and k are equal.

Since line l is perpendicular to line k, their slopes are negative reciprocals of each other, and thus the product of their slopes is -1.

For example, if the slope of line k = 2/3, then the slope of line l, which is perpendicular to line k, is -3/2. The product of their slopes is (2/3) x (-3/2) = -1. This is a property of any two lines that are perpendicular to each other, as long as the slope of neither line is 0.

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Re: If line l is perpendicular to line k, which of the following must be   [#permalink] 21 Jan 2019, 19:06
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