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Perpendicular lines m and n intersect at point (a, b), [#permalink]
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 xintercept of line m is positive. ❑ The yintercept of line m is negative ❑ The xintercept of line n is positive. ❑ The yintercept of line n is negative. ❑ The product of the x and yintercepts of line m is not positive, ❑ The sum of the xintercepts of lines m and n is positive.
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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink]
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]
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 xintercept 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]
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 xintercept 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]
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 xintercept of line m is positive. ❑ The yintercept of line m is negative ❑ The xintercept of line n is positive. ❑ The yintercept of line n is negative. ❑ The product of the x and yintercepts of line m is not positive, ❑ The sum of the xintercepts of lines m and n is positive. Please explain why A & F are not correct?



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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink]
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 01



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Re: Perpendicular lines m and n intersect at point (a, b), [#permalink]
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 xintercept 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]
05 Jan 2019, 20:36
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 xintercept of line m is positive. ❑ The yintercept of line m is negative ❑ The xintercept of line n is positive. ❑ The yintercept of line n is negative. ❑ The product of the x and yintercepts of line m is not positive, ❑ The sum of the xintercepts 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 yintercept both negative and positive, so eliminate A, B and F.. Line n  We can see that the x intercept and yintercept both will be positive.. So, C and E are true and eliminate D ans C and E
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Some useful Theory. 1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressionsarithmeticgeometricandharmonic11574.html#p27048 2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effectsofarithmeticoperationsonfractions11573.html?sid=d570445335a783891cd4d48a17db9825 3. Remainders : https://greprepclub.com/forum/remainderswhatyoushouldknow11524.html 4. Number properties : https://greprepclub.com/forum/numberpropertyallyourequire11518.html 5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolutemodulusabetterunderstanding11281.html




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