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In the rectangular coordinate system above, if OP < PQ, is

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Re: In the rectangular coordinate system above, if OP < PQ, is [#permalink]

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New post 17 Jul 2015, 06:46
So, we have OP<PQ, Area of OPQ = (PS*OQ) / 2 > 48 --> PS*OQ > 96 ?

1) P (6,8) means --> Heght PS=8, OS=6 then we can find OP^2=8^2+6^2=100, OP=10
Since PQ>OP --> SQ>6 (SQ^2=PQ^2 (let's say 10,1) - 64 means SQ>6) --> OQ>12 -> 8*OQ(>12) > 96 SUFFICIENT
2) We need the height to be able to calculate the area - INSUFFICIENT
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Re: In the rectangular coordinate system above, if OP < PQ, is [#permalink]

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New post 05 Oct 2015, 03:57
Bunuel wrote:
Kriti2013 wrote:
Hi,

Could you explain the following :

Since OP<PQ then OS<SQ and the base OQ is more than 12


Thanks.


Since OS=6 and OS<SQ, then SQ>6, thus OQ=OS+SQ=6+(more than 6)=(more than 12).

Hope it's clear.


Hi Bunuel,

Could you explain why OS < SQ? is there a theory/concept behind it?
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Re: In the rectangular coordinate system above, if OP < PQ, is [#permalink]

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New post 05 Oct 2015, 05:37
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harishbiyani8888 wrote:
Bunuel wrote:
Kriti2013 wrote:
Hi,

Could you explain the following :

Since OP<PQ then OS<SQ and the base OQ is more than 12


Thanks.


Since OS=6 and OS<SQ, then SQ>6, thus OQ=OS+SQ=6+(more than 6)=(more than 12).

Hope it's clear.


Hi Bunuel,

Could you explain why OS < SQ? is there a theory/concept behind it?


Image

PS^2 + OS^2 = OP^2
PS^2 + SQ^2 = PQ^2

Since we are given that OP < PQ, then OS < SQ.

Hope it's clear.
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Re: In the rectangular coordinate system above, if OP < PQ, is [#permalink]

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New post 11 Sep 2017, 23:13
Hi Bunuel,

For statement 2, Is it possible to solve by using sides of triangle properties ( third side less than sum of the other two and greater than the difference of other two?

Thanks for your help.

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Re: In the rectangular coordinate system above, if OP < PQ, is [#permalink]

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New post 11 Sep 2017, 23:37
artisood1707 wrote:
Hi Bunuel,

For statement 2, Is it possible to solve by using sides of triangle properties ( third side less than sum of the other two and greater than the difference of other two?

Thanks for your help.

Posted from my mobile device


Don't see how it can give you the answer. Can you please show what are you trying to do?
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In the rectangular coordinate system above, if OP < PQ, is [#permalink]

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New post 11 Sep 2017, 23:59
eybrj2 wrote:
Image
In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ?

(1) The coordinates of point P are (6,8)

(2) The coordinates of point Q are (13,0)

[Reveal] Spoiler:
Attachment:
Triangle.png


Let us say OP=PQ
1) P= 6,8
OP =10
PQ=10 we have assumed
=> Q = 12,0

A= 0.5 x 8 x 12 =48
But it is given OP < PQ => A<48 DEFINITE NO
Sufficient
2) Q= 13,0
Insufficient as it will depend upon height ie y coordinate of P
if y coordinate of p < 96/13 then only above false => if y coord of P > 96/13 above is true
we dont know y coord of P => INSUFFICIENT


ANSWER IS A
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In the rectangular coordinate system above, if OP < PQ, is   [#permalink] 11 Sep 2017, 23:59

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