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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
For any triangle T in the xycoordinate plan, the center of T is defin
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18 Sep 2022, 21:48
18 Sep 2022, 21:48
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Question Stats:
75% (00:44) correct
25% (01:17) wrong based on 4 sessions
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For any triangle T in the xy–coordinate plan, the center of T is defined to be the point whose x–coordinate is the average (arithmetic mean) of the x–coordinates of the vertices of T and whose y–coordinate is the average of the y–coordinates of the vertices of T. If a certain triangle has vertices at the points (0,0) and (6,0) and center at the point (3,2), what are the coordinates of the remaining vertex?
A. (3,4)
B. (3,6)
C. (4,9)
D. (6,4)
E. (9,6)
A. (3,4)
B. (3,6)
C. (4,9)
D. (6,4)
E. (9,6)
Re: For any triangle T in the xycoordinate plan, the center of T is defin
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21 Sep 2022, 05:06
21 Sep 2022, 05:06
Expert Reply
Great question. The best mode of attack is to Dive In.
Let's start by labeling the three vertices of triangle T as a, b, and c. We know pt a is at (0,0), b is at (6,0), and c is unknown, (cx, cy).
The center, as defined in the problem, is the arithmetic mean of the x and y coordinates individually. Let's write that out as a formula, where the center of triangle T is labeled as pt m at (mx, my).
mx = (ax + bx + cx)/3
my = (ay + by + cy)/3
We know from the problem that pt m is at (3,2), so let's plug in first for the x-coordinate, cx:
3 = (0 + 6 + cx)/3
With some arithmetic, we can solve this to see that cx = 3.
Now, let's do the same for the y-coordinate, cy:
2 = (0 + 0 + cy)/3
So... cy = 6.
Putting these together, we now have that the coordinate of the missing vertex is at (cx, cy), or (3,6)... Answer Choice B.
Let's start by labeling the three vertices of triangle T as a, b, and c. We know pt a is at (0,0), b is at (6,0), and c is unknown, (cx, cy).
The center, as defined in the problem, is the arithmetic mean of the x and y coordinates individually. Let's write that out as a formula, where the center of triangle T is labeled as pt m at (mx, my).
mx = (ax + bx + cx)/3
my = (ay + by + cy)/3
We know from the problem that pt m is at (3,2), so let's plug in first for the x-coordinate, cx:
3 = (0 + 6 + cx)/3
With some arithmetic, we can solve this to see that cx = 3.
Now, let's do the same for the y-coordinate, cy:
2 = (0 + 0 + cy)/3
So... cy = 6.
Putting these together, we now have that the coordinate of the missing vertex is at (cx, cy), or (3,6)... Answer Choice B.
gmatclubot
Re: For any triangle T in the xycoordinate plan, the center of T is defin [#permalink]
21 Sep 2022, 05:06
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