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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]  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
C,E
[Reveal] Spoiler: OA

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