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Perpendicular lines m and n intersect at point (a, b),

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Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   06 Aug 2017, 10:27
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Perpendicular lines m and n intersect at point (a, b), where a > b > 0. The slope of line m is between 0 and 1. Which of the following statements MUST be true ?

Indicate all such statements.

❑ The x-intercept of line m is positive.

❑ The y-intercept of line m is negative

❑ The x-intercept of line n is positive.

❑ The y-intercept of line n is negative.

❑ The product of the x- and y-intercepts of line m is not positive,

❑ The sum of the x-intercepts of lines m and n is positive.
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C,E
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Avraheem
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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   27 Jun 2018, 07:13
Hello guys. Why (A) and (F) are not true? How you broach the solution here?
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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   01 Jul 2018, 20:31
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Avraheem wrote:
Hello guys. Why (A) and (F) are not true? How you broach the solution here?



Hello Avraheem,

I hope you are aware with x- intercept, y- intercept, slope of a line, Positive slop and negative slope

Back to the question:

Here the line m is a positve slop and it lies between 0 and 1 and we know that the slope of one perpendicular line is negative reciprocal of the other

So if slope of m = 1 then the slope of line n = \(-\frac{1}{1}\) =\(-1\)

Option A and Option F: The x intercept may not be always positive. We are given that the slope of the line m is positive and lies between 0 and 1. For this x intercept can be negative, positive or zero, whereas the y intercept always remain positive.

For the line n the x intercept and y intercept will always be positive

As there are are no. of possibility of x-intercept for line m ; so option F is also not correct
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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   21 Jul 2018, 23:16
pranab01 wrote:
Avraheem wrote:
Hello guys. Why (A) and (F) are not true? How you broach the solution here?



Hello Avraheem,

I hope you are aware with x- intercept, y- intercept, slope of a line, Positive slop and negative slope

Back to the question:

Here the line m is a positve slop and it lies between 0 and 1 and we know that the slope of one perpendicular line is negative reciprocal of the other

So if slope of m = 1 then the slope of line n = \(-\frac{1}{1}\) =\(-1\)

Option A and Option F: The x intercept may not be always positive. We are given that the slope of the line m is positive and lies between 0 and 1. For this x intercept can be negative, positive or zero, whereas the y intercept always remain positive.

For the line n the x intercept and y intercept will always be positive

As there are are no. of possibility of x-intercept for line m ; so option F is also not correct


Thanks a lot. Last question, why line m can not pass through (0,0), which is neither positive nor negative?
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ShubhiNigam29
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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   05 Aug 2018, 04:26
Carcass wrote:

This question is part of GREPrepClub - The Questions Vault Project



Perpendicular lines m and n intersect at point (a, b), where a > b > 0. The slope of line m is between 0 and 1. Which of the following statements MUST be true ?

Indicate all such statements.

❑ The x-intercept of line m is positive.

❑ The y-intercept of line m is negative

❑ The x-intercept of line n is positive.

❑ The y-intercept of line n is negative.

❑ The product of the x- and y-intercepts of line m is not positive,

❑ The sum of the x-intercepts of lines m and n is positive.

Show: :: OA
C,E


Please explain why A & F are not correct?
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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   05 Jan 2019, 17:15
Avraheem wrote:

Thanks a lot. Last question, why line m can not pass through (0,0), which is neither positive nor negative?


Because the slope is between 0-1
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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   05 Jan 2019, 17:17
ShubhiNigam29 wrote:

Please explain why A & F are not correct?


Check this

pranab01 wrote:

Option A and Option F: The x intercept may not be always positive. We are given that the slope of the line m is positive and lies between 0 and 1. For this x intercept can be negative, positive or zero, whereas the y intercept always remain positive.

For the line n the x intercept and y intercept will always be positive

As there are are no. of possibility of x-intercept for line m ; so option F is also not correct
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chetan2u
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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   05 Jan 2019, 20:36
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Carcass wrote:

This question is part of GREPrepClub - The Questions Vault Project



Perpendicular lines m and n intersect at point (a, b), where a > b > 0. The slope of line m is between 0 and 1. Which of the following statements MUST be true ?

Indicate all such statements.

❑ The x-intercept of line m is positive.

❑ The y-intercept of line m is negative

❑ The x-intercept of line n is positive.

❑ The y-intercept of line n is negative.

❑ The product of the x- and y-intercepts of line m is not positive,

❑ The sum of the x-intercepts of lines m and n is positive.


You can draw a sketch to be more clear on the regions these lines can be formed
Look at the attached figure..
(I) The red line is where a=b but a>b>0, so the point will lie below this line...
(II) A point (a,b) is taken and the light grey colour is the portion wher line m can exist passing through (a,b) and GREEN portion is wher line n can exist.

Line m - As we can see it can have x intercept and y-intercept both negative and positive, so eliminate A, B and F..
Line n - We can see that the x intercept and y-intercept both will be positive.. So, C and E are true and eliminate D

ans C and E
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ashhadbgmail
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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   20 Mar 2023, 02:46
❑ The product of the x- and y-intercepts of line m is not positive,

this line can pass through the origin also
if you shift the line without changing its slope, it can be seen that it can pass through
the origin and thus
the product can be zero, i.e neither positive nor negative

plz comment
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emmar
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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   28 Dec 2023, 12:33
ashhadbgmail wrote:
❑ The product of the x- and y-intercepts of line m is not positive,

this line can pass through the origin also
if you shift the line without changing its slope, it can be seen that it can pass through
the origin and thus
the product can be zero, i.e neither positive nor negative

plz comment


Are you asking a question? Because you're right. Product can be zero, or it can be negative. But not positive.
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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink]
28 Dec 2023, 12:33
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