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Shortest distance between 2 parallel lines

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Shortest distance between 2 parallel lines

by gmattesttaker2 » Sat Feb 22, 2014 10:06 pm
Hello,

Can you please assist with this:

In the rectangular coordinate system above, if the equation of l1 is y = x and l1 is parallel to l2, what is the shortest distance between l1 and l2?

A) sq. root (2)
B) 1
C) sq. root (2)/2
D) 1/2
E) 1/4

OA: C

Thanks a lot,
Sri
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by theCodeToGMAT » Sat Feb 22, 2014 10:29 pm
[spoiler]{C}[/spoiler]
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by ajaysingh24 » Sun Feb 23, 2014 2:15 am
1/sqrt(2)
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by gmattesttaker2 » Thu Feb 27, 2014 10:13 pm
theCodeToGMAT wrote:[spoiler]{C}[/spoiler]
Hi Rahul,

Thanks for the diagram. I was just wondering if the x axis distance between l1 and l2 can be less than 1 say something like 0.5?

Thanks,
Sri
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by theCodeToGMAT » Thu Feb 27, 2014 10:27 pm
gmattesttaker2 wrote:
theCodeToGMAT wrote:[spoiler]{C}[/spoiler]
Hi Rahul,

Thanks for the diagram. I was just wondering if the x axis distance between l1 and l2 can be less than 1 say something like 0.5?

Thanks,
Sri
Hello Sri,

In the question stem, we are provided with the information that both lines are 1 unit apart on x-axis.

The diagram forms a 45-90-45 triangle; the basic property of this triangle is

Image

Where, "m" can be any integer value.

Considering this fact in the question, m = 1.. So, (1)/sqrt(2) or sqrt(2)/2
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by gmattesttaker2 » Thu Feb 27, 2014 10:53 pm
theCodeToGMAT wrote:
gmattesttaker2 wrote:
theCodeToGMAT wrote:[spoiler]{C}[/spoiler]
Hi Rahul,

Thanks for the diagram. I was just wondering if the x axis distance between l1 and l2 can be less than 1 say something like 0.5?

Thanks,
Sri
Hello Sri,

In the question stem, we are provided with the information that both lines are 1 unit apart on x-axis.

The diagram forms a 45-90-45 triangle; the basic property of this triangle is

Image

Where, "m" can be any integer value.

Considering this fact in the question, m = 1.. So, (1)/sqrt(2) or sqrt(2)/2
Hello Rahul,

Thanks for the explanation. Sorry I totally overlooked the 1 unit distance in the original diagram. Just one more question. How do we know that side opposite angle A is equal to the side opposite angle B. Does it have anything to do with the traversal passing through the parallel lines l1 and l2? I was mainly not sure how do we know that both the base angles are 45 degrees? Thanks a lot for your help.

Best Regards,
Sri
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by theCodeToGMAT » Thu Feb 27, 2014 11:07 pm
gmattesttaker2 wrote: Hello Rahul,

Thanks for the explanation. Sorry I totally overlooked the 1 unit distance in the original diagram. Just one more question. How do we know that side opposite angle A is equal to the side opposite angle B. Does it have anything to do with the traversal passing through the parallel lines l1 and l2? I was mainly not sure how do we know that both the base angles are 45 degrees? Thanks a lot for your help.

Best Regards,
Sri
Sri, please refer the attached image.
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