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# Which of the following lines are perpendicular to the line y=x in the

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Joined: 02 Sep 2009
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Which of the following lines are perpendicular to the line y=x in the  [#permalink]

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20 May 2019, 04:16
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Difficulty:

25% (medium)

Question Stats:

67% (00:48) correct 33% (01:25) wrong based on 36 sessions

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Which of the following lines are perpendicular to the line y=x in the xy-plane?

I. x + y = 0
II. x + y = 1
III. x - y = 2

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

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Re: Which of the following lines are perpendicular to the line y=x in the  [#permalink]

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20 May 2019, 05:49
Bunuel wrote:
Which of the following lines are perpendicular to the line y=x in the xy-plane?

I. x + y = 0
II. x + y = 1
III. x - y = 2

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

The two lines are perpendicular if the product of their slopes is equal to -1 i.e. $$m_1*m_2 = -1$$

Line y=x has slope = 1 . [by comparing it with general equation of line i.e. y = mx+c]
i.e. $$1*m_2 = -1$$
i.e. $$m_2 = -1$$

i.e. line with -1 slope will be perpendicular to the given line

I. x + y = 0 slope = -1
II. x + y = 1 slope = -1
III. x - y = 2 slope = 1

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Re: Which of the following lines are perpendicular to the line y=x in the  [#permalink]

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21 May 2019, 19:28
Bunuel wrote:
Which of the following lines are perpendicular to the line y=x in the xy-plane?

I. x + y = 0
II. x + y = 1
III. x - y = 2

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

Perpendicular lines have slopes that are negative reciprocals of each other. Since the given line has a slope of 1, any line perpendicular to it has a slope of -1.

Thus, we see that I and II are correct since we have y = -x and y = -x + 1, respectively (notice that each has a slope of -1).

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Re: Which of the following lines are perpendicular to the line y=x in the  [#permalink]

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21 May 2019, 19:45
Bunuel wrote:
Which of the following lines are perpendicular to the line y=x in the xy-plane?

I. x + y = 0
II. x + y = 1
III. x - y = 2

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

For two st. lines in the form y=mx +c
If mi*m2= -1 Then perpendicular
m1=m2 then parallel.

given line m=1

Let's find m for
Line I (-1) Perpendicular
Line II (-1) Perpendicular
Line III (1) Parallel

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Re: Which of the following lines are perpendicular to the line y=x in the   [#permalink] 21 May 2019, 19:45
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