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Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista

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Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista [#permalink] New post   Updated on: 29 Oct 2014, 08:37
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Point K = (A,0), Point G = (2A + 4, \(\sqrt{2A+ 9}\)). Is the distance between point K and G prime?

(1) A^2 – 5A – 6 = 0
(2) A > 2
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C

Originally posted by sambam on 10 Jan 2013, 09:55.
Last edited by Bunuel on 29 Oct 2014, 08:37, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista [#permalink] New post   10 Jan 2013, 16:51
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Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the distance between point K and G prime?

The formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\).

Hence, the distance between points G and K is \(d=\sqrt{(2A+4-A)^2+(\sqrt{2A+9}-0)^2}=\sqrt{(A+5)^2}=|A+5|\)

(1) A^2 – 5A – 6 = 0 --> \((A-6)(A+1)=0\) --> \(A=6\) or \(A=-1\) --> \(d=|A+5|=11=prime\) or \(d=|A+5|=4\neq{prime}\). Not sufficient.

(2) A > 2. If \(A=3\), then \(d=|A+5|=8\neq{prime}\) but if \(A=6\), then \(d=|A+5|=11=prime\). Not sufficient.

(1)+(2) Since from (2) A > 2, then from (1) \(A=6\), thus \(d=|A+5|=11=prime\). Sufficient.

Answer: C.

Hope it's clear.
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Re: Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista [#permalink] New post   30 Mar 2017, 22:52
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sambam wrote:
Point K = (A,0), Point G = (2A + 4, \(\sqrt{2A+ 9}\)). Is the distance between point K and G prime?

(1) \(A^2 – 5A – 6 = 0\)
(2) \(A > 2\)


Bunuel, Original Source is Manhattan Prep. Please help to edit. Thank you.
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Re: Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista [#permalink] New post   30 Mar 2017, 23:29
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ziyuen wrote:
sambam wrote:
Point K = (A,0), Point G = (2A + 4, \(\sqrt{2A+ 9}\)). Is the distance between point K and G prime?

(1) \(A^2 – 5A – 6 = 0\)
(2) \(A > 2\)


Bunuel, Original Source is Manhattan Prep. Please help to edit. Thank you.


Edited. Thank you.
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Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista [#permalink] New post   20 Jun 2018, 05:03
Bunuel, can you please show, how you simplified

d=(2A+4−A)2+(2A+9−−−−−−√−0)2−−−−−−−−−−−−−−−−−−−−−−−−−√=(A+5)2−−−−−−−√=|A+5|d=(2A+4−A)2+(2A+9−0)2=(A+5)2=|A+5|
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Re: Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista [#permalink] New post   20 Jun 2018, 05:10
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gsingh0711 wrote:
Bunuel, can you please show, how you simplified

d=(2A+4−A)2+(2A+9−−−−−−√−0)2−−−−−−−−−−−−−−−−−−−−−−−−−√=(A+5)2−−−−−−−√=|A+5|d=(2A+4−A)2+(2A+9−0)2=(A+5)2=|A+5|


\(d=\sqrt{(2A+4-A)^2+(\sqrt{2A+9}-0)^2}=\sqrt{(A+4)^2+(\sqrt{2A+9})^2}=\)

\(=\sqrt{(A^2+8A+16)+(2A+9)}=\sqrt{A^2+10A+25}=\sqrt{(A+5)^2}=|A+5|\)
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Re: Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista [#permalink] New post   16 Aug 2023, 12:44
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Re: Point K = (A,0), Point G = (2A + 4, sqrt2A+ 9). Is the dista [#permalink]
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