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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.
[Reveal] Spoiler: OA

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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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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post 05 Aug 2018, 04:26
Carcass wrote:


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.

[Reveal] Spoiler: 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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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post 05 Jan 2019, 20:36
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Expert's post
Carcass wrote:


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
Attachments

00000.png
00000.png [ 33.32 KiB | Viewed 3239 times ]


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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: Perpendicular lines m and n intersect at point (a, b),   [#permalink] 05 Jan 2019, 20:36
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