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# What will be the coordinates of the new origin if the coordinates of a

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What will be the coordinates of the new origin if the coordinates of a  [#permalink]

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06 Jun 2020, 18:06
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GMATBusters’ Quant Quiz Question 4

What will be the coordinates of the new origin if the coordinates of a point (17, 29) become (4, 17) after shifting the origin?

A. (-9,10)
B. (-11, 12)
C. (9,14)
D. (13,12)
E. (12,15)

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Re: What will be the coordinates of the new origin if the coordinates of a  [#permalink]

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06 Jun 2020, 18:27
If origin shifts to (x,y), then Co-ordinates (17,29) become (4,17) then,
17- x = 4 and 29-y=17 (Although i am not 100% sure)
x =13 & y=12

Imo. D.
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Re: What will be the coordinates of the new origin if the coordinates of a  [#permalink]

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06 Jun 2020, 18:38
Let new origin (x,y)
17-x=4
x=13
29-y=17
y=12
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Re: What will be the coordinates of the new origin if the coordinates of a  [#permalink]

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06 Jun 2020, 19:14
The distance between (17,29) and one of the answer choices should be equal to the distance between (4,17) and the origin.
Distance= Square root of sum of difference between the x and y co-ordinates. Using the answer choices, the only choice that fits is (13,12).
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Re: What will be the coordinates of the new origin if the coordinates of a  [#permalink]

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06 Jun 2020, 20:25
coordinates 17,29 ( h,k) become 4,17 ( x,y)

change in distance ; 17-4 ; 29-17 ; 13,12
OPTION D
What will be the coordinates of the new origin if the coordinates of a point (17, 29) become (4, 17) after shifting the origin?

A. (-9,10)
B. (-11, 12)
C. (9,14)
D. (13,12)
E. (12,15)
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Re: What will be the coordinates of the new origin if the coordinates of a  [#permalink]

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06 Jun 2020, 21:12
What will be the coordinates of the new origin if the coordinates of a point (17, 29) become (4, 17) after shifting the origin?

A. (-9,10)
B. (-11, 12)
C. (9,14)
D. (13,12)
E. (12,15)

Since (17, 29) means 17 units in the positive x-direction and 29 units in the positive y-direction.

(4, 17) means 4 units in the positive x-direction and 17 unit in the positive y-direction from the new origin

Therefore, the new coordinate of the origin will be ((17-4) = 13, (29-17) = 12) or (13,12) so option D is the correct answer
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Re: What will be the coordinates of the new origin if the coordinates of a  [#permalink]

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06 Jun 2020, 21:53
New coordinates when origin is shifted to (x,y)are(Xnew,Ynew)=(Xold−x,Yold−y)
(Xold,Yold) = 17,29
(x,y)=(X,Y) {coordinate of new origin}
(Xnew,Ynew) = 4,17

=> (4,17)=(17-x)(29-y)
=> 4=17-x => X=13
=> 17=29-y => Y = 12

THE CORDINATES OF NEW ORIGIN = (13,12)

Posted from my mobile device
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Re: What will be the coordinates of the new origin if the coordinates of a  [#permalink]

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06 Jun 2020, 22:01
the difference in x and y co-ordinate respectively of the original and shifted co-ordinates is the answer
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Re: What will be the coordinates of the new origin if the coordinates of a  [#permalink]

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06 Jun 2020, 23:45
Asked: What will be the coordinates of the new origin if the coordinates of a point (17, 29) become (4, 17) after shifting the origin?

A. (-9,10)
B. (-11, 12)
C. (9,14)
D. (13,12)
E. (12,15)

x' = 4 = 17-13 = x - 13
y' = 17 = 29 - 12 = y - 12

Coordinates of new origin = (13,12)

IMO D
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Re: What will be the coordinates of the new origin if the coordinates of a  [#permalink]

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06 Jun 2020, 23:47
Quote:
What will be the coordinates of the new origin if the coordinates of a point (17, 29) become (4, 17) after shifting the origin?

A. (-9,10)
B. (-11, 12)
C. (9,14)
D. (13,12)
E. (12,15)

D , IMO

New Origin = 17-4 ,29-17 = (13,12)
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Re: What will be the coordinates of the new origin if the coordinates of a  [#permalink]

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07 Jun 2020, 01:30
Consider a simple example.

1) A and B are two persons 17km apart.

|<-----------17------------>|
$$A\quad \quad \quad \quad \quad \quad \quad \quad B$$

Now, B has a broken leg and can't walk. So, A walks and stays at a distance of 4 km from B.

$$\quad \quad \quad \quad$$|<-----4----->|
$$\quad \quad \quad \; A \quad \quad \quad \quad \quad B$$

Now, how much distance did A walk? 13kms.

Just replace A with the Origin(0,0) and B with the coordinates of the point. The origin moved 13units to the right(X-axis) to make B 4kms away from it ----(1)

2) X & Y are two persons 29kms apart.

|<-----------29------------>|
$$X\quad \quad \quad \quad \quad \quad \quad \quad Y$$

Now, X is spying on Y. So, X needs to get close and be at a distance of 17kms so as to watch Y with powerful binaculars. (Those are military grade, so can zoom 17x kms)

$$\quad \quad \quad \quad$$|<-----17----->|
$$\quad \quad \quad \; X \quad \quad \quad \quad \quad Y$$

Now, how much distance did X go? 12kms. Lets just say instead East to West, X & Y are aligned South to North.
Thus, X moved 12 units North.

Just replace X with the Origin(0,0) and Y with the coordinates of the point. The origin moved 12 units to the North(Y-axis) to make Y 17units from it ----(2)

Combining (1) & (2), The origin moved 13units in positive X axis & 12units in positive Y axis. Thus the origin now is at (13,12) at a safe distance spying on Y.
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Re: What will be the coordinates of the new origin if the coordinates of a  [#permalink]

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07 Jun 2020, 04:54
Old point (x,y) wrt (0,0) origin
New point (X,Y) wrt (h,k) new origin
Thus x=X+h and y=Y+k

(x,y)= (17,29)
(X,Y)=(4,17)

Thus by putting values we get (h,k) new origin is (13,12)

IMO ans is D
Re: What will be the coordinates of the new origin if the coordinates of a   [#permalink] 07 Jun 2020, 04:54