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Perpendicular lines m and n intersect at point (a, b),
[#permalink]
06 Aug 2017, 10:27

3

Expert Reply

Question Stats:

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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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?

Re: Perpendicular lines m and n intersect at point (a, b),
[#permalink]
01 Jul 2018, 20:31

2

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?

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.

Show: :: OA

C,E

Please explain why A & F are not correct?

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 0-1

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 x-intercept for line m ; so option F is also not correct

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

1

Expert Reply

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

00000.png [ 33.32 KiB | Viewed 4813 times ]

_________________

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