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Points A = (3,9), B = (1,1), C = (5,3), and D=(a,b) lie in the first

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Bunuel
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Points A = (3,9), B = (1,1), C = (5,3), and D=(a,b) lie in the first [#permalink] New post   18 Mar 2019, 02:58
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Points A = (3,9), B = (1,1), C = (5,3), and D=(a,b) lie in the first quadrant and are the vertices of quadrilateral ABCD. The quadrilateral formed by joining the midpoints of AB, BC, CD, and DA is a square. What is the sum of the coordinates of point D?

(A) 7
(B) 9
(C) 10
(D) 12
(E) 16
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C
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GMATinsight
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Re: Points A = (3,9), B = (1,1), C = (5,3), and D=(a,b) lie in the first [#permalink] New post   18 Mar 2019, 04:25
Expert Reply
Bunuel wrote:
Points A = (3,9), B = (1,1), C = (5,3), and D=(a,b) lie in the first quadrant and are the vertices of quadrilateral ABCD. The quadrilateral formed by joining the midpoints of AB, BC, CD, and DA is a square. What is the sum of the coordinates of point D?

(A) 7
(B) 9
(C) 10
(D) 12
(E) 16


Check the video solution as mentioned below



Answer: Option C
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Screenshot 2019-03-18 at 4.51.57 PM.png
Screenshot 2019-03-18 at 4.51.57 PM.png [ 864.39 KiB | Viewed 3998 times ]

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Re: Points A = (3,9), B = (1,1), C = (5,3), and D=(a,b) lie in the first [#permalink] New post   18 Mar 2019, 06:11
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Bunuel wrote:
Points A = (3,9), B = (1,1), C = (5,3), and D=(a,b) lie in the first quadrant and are the vertices of quadrilateral ABCD. The quadrilateral formed by joining the midpoints of AB, BC, CD, and DA is a square. What is the sum of the coordinates of point D?

(A) 7
(B) 9
(C) 10
(D) 12
(E) 16


It can get done in a minute if you follow the logic discussed here:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/0 ... ry-part-i/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/0 ... y-part-ii/

Now, look at the diagram below:

Attachment:
Screenshot 2019-03-18 at 18.40.37.png
Screenshot 2019-03-18 at 18.40.37.png [ 503.47 KiB | Viewed 3879 times ]


Plot the 3 co-ordinates (A, B and C) of the given quad and find their mid points to get two co-ordinates of the square (N and M). Now MP will be another side of the square such that it is perpendicular and of the same length as MN.

Hence MX = 3 = MY
NX = 1 = PY

So point P will be 3 to the right of M and 1 above M i.e. at (5, 6).
P will be the mid point of AD and hence D will be (7, 3).

Sum of the coordinates of D = 7+3 = 10

Answer (C)
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Re: Points A = (3,9), B = (1,1), C = (5,3), and D=(a,b) lie in the first [#permalink] New post   19 Mar 2019, 02:59
VeritasKarishma wrote:
Bunuel wrote:
Points A = (3,9), B = (1,1), C = (5,3), and D=(a,b) lie in the first quadrant and are the vertices of quadrilateral ABCD. The quadrilateral formed by joining the midpoints of AB, BC, CD, and DA is a square. What is the sum of the coordinates of point D?

(A) 7
(B) 9
(C) 10
(D) 12
(E) 16


It can get done in a minute if you follow the logic discussed here:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/0 ... ry-part-i/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/0 ... y-part-ii/

Now, look at the diagram below:

Attachment:
Screenshot 2019-03-18 at 18.40.37.png


Plot the 3 co-ordinates (A, B and C) of the given quad and find their mid points to get two co-ordinates of the square (N and M). Now MP will be another side of the square such that it is perpendicular and of the same length as MN.

Hence MX = 3 = MY
NX = 1 = PY

So point P will be 3 to the right of M and 1 above M i.e. at (5, 6).
P will be the mid point of AD and hence D will be (7, 3).

Sum of the coordinates of D = 7+3 = 10

Answer (C)


Hi

I am unable to understand the below points.

Hence MX = 3 = MY
NX = 1 = PY

So point P will be 3 to the right of M and 1 above M i.e. at (5, 6).

Could you please explain in detail about the solution ?

Thanks
Sekhar
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KarishmaB
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Re: Points A = (3,9), B = (1,1), C = (5,3), and D=(a,b) lie in the first [#permalink] New post   19 Mar 2019, 03:12
Expert Reply
sekharm2389 wrote:
VeritasKarishma wrote:
Bunuel wrote:
Points A = (3,9), B = (1,1), C = (5,3), and D=(a,b) lie in the first quadrant and are the vertices of quadrilateral ABCD. The quadrilateral formed by joining the midpoints of AB, BC, CD, and DA is a square. What is the sum of the coordinates of point D?

(A) 7
(B) 9
(C) 10
(D) 12
(E) 16


It can get done in a minute if you follow the logic discussed here:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/0 ... ry-part-i/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/0 ... y-part-ii/

Now, look at the diagram below:

Attachment:
Screenshot 2019-03-18 at 18.40.37.png


Plot the 3 co-ordinates (A, B and C) of the given quad and find their mid points to get two co-ordinates of the square (N and M). Now MP will be another side of the square such that it is perpendicular and of the same length as MN.

Hence MX = 3 = MY
NX = 1 = PY

So point P will be 3 to the right of M and 1 above M i.e. at (5, 6).
P will be the mid point of AD and hence D will be (7, 3).

Sum of the coordinates of D = 7+3 = 10

Answer (C)


Hi

I am unable to understand the below points.

Hence MX = 3 = MY
NX = 1 = PY

So point P will be 3 to the right of M and 1 above M i.e. at (5, 6).

Could you please explain in detail about the solution ?

Thanks
Sekhar


I am guessing you did not go through the two links I gave above. The logic of why MY will be 3 and PY will be 1 is explained in them in detail. Without checking the two posts, you will not be able to understand this solution. Please do go through them and then let me know if it makes sense.
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Re: Points A = (3,9), B = (1,1), C = (5,3), and D=(a,b) lie in the first [#permalink] New post   20 Dec 2022, 07:49
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Re: Points A = (3,9), B = (1,1), C = (5,3), and D=(a,b) lie in the first [#permalink]
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