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# If the distance from P to O in the figure above is k, then what is the

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Math Expert
Joined: 02 Sep 2009
Posts: 58395
If the distance from P to O in the figure above is k, then what is the  [#permalink]

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18 Nov 2016, 03:57
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25% (medium)

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74% (01:22) correct 26% (01:44) wrong based on 241 sessions

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If the distance from P to O in the figure above is k, then what is the distance from O to point Q (not shown), whose coordinates are (4x, 4y)?

A. k/2
B. 2k
C. 4k
D. 8k
E. 16k

Attachment:

T6194.png [ 4 KiB | Viewed 2059 times ]

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Re: If the distance from P to O in the figure above is k, then what is the  [#permalink]

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18 Nov 2016, 04:16
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Bunuel wrote:

If the distance from P to O in the figure above is k, then what is the distance from O to point Q (not shown), whose coordinates are (4x, 4y)?

A. k/2
B. 2k
C. 4k
D. 8k
E. 16k

Attachment:
T6194.png

Given x^2+y^2= K^2 since distance between (0,0) and (x,y)= k
distance between (0,0) and (4x,4y) = (4x)^2 + (4y)^2 = 16K^2
hence distance between (0,0) and (4x,4y)= 4k
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Re: If the distance from P to O in the figure above is k, then what is the  [#permalink]

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04 May 2017, 10:11
Bunuel wrote:

If the distance from P to O in the figure above is k, then what is the distance from O to point Q (not shown), whose coordinates are (4x, 4y)?

A. k/2
B. 2k
C. 4k
D. 8k
E. 16k

Attachment:
T6194.png

Using hypotenuse formula,
for coordinates (x,y),
x^2 + y^2 = k^2

for coordinates (4x,4y),
16x^2 + 16y^2 = 16 (x^2 + y^2) = 16k^2

So the hypotenuse will be 4k
Manager
Joined: 14 Sep 2016
Posts: 59
Concentration: Finance, Economics
If the distance from P to O in the figure above is k, then what is the  [#permalink]

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04 May 2017, 12:18
Bunuel wrote:

If the distance from P to O in the figure above is k, then what is the distance from O to point Q (not shown), whose coordinates are (4x, 4y)?

A. k/2
B. 2k
C. 4k
D. 8k
E. 16k

Attachment:
The attachment T6194.png is no longer available

Assign values

X=1
Y=1
O to P = 1k
O to Q = 4x the length, 4k.
Attachments

Untitled.png [ 5.66 KiB | Viewed 1276 times ]

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Re: If the distance from P to O in the figure above is k, then what is the  [#permalink]

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15 May 2017, 13:18
C

SQR of x^2 + y^2 = k

SQR of (4x)^2 + (4y)^2 = 4 * (SQR of x^2 + y^2) =4k
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Re: If the distance from P to O in the figure above is k, then what is the  [#permalink]

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24 Sep 2018, 08:11
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Re: If the distance from P to O in the figure above is k, then what is the   [#permalink] 24 Sep 2018, 08:11
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