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# for any triangle T in the xy-cordinate plane, the centre of

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Manager
Joined: 23 Jan 2008
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for any triangle T in the xy-cordinate plane, the centre of [#permalink]  04 Feb 2008, 14:42
for any triangle T in the xy-cordinate plane, the centre of T is defined a to be the point whose x-cordinate is the average of the x-cordinate of the vertices of T and whose Y-cordinate is the average of the y-cordinates of the vertices of T. If a certain triangle has vertices at the point (0,0)and (6,0) and centre at the point (3,2), what are the cordinates of the remainig vertex ?

1. (3,4)
2. (3,6)
3. (4,9)
4. (6,4)
5. (9,6)
Senior Manager
Joined: 29 Nov 2006
Posts: 321
Location: Orange County, CA
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Re: any triangle T ? [#permalink]  04 Feb 2008, 15:31
Quote:
for any triangle T in the xy-cordinate plane, the centre of T is defined a to be the point whose x-cordinate is the average of the x-cordinate of the vertices of T and whose Y-cordinate is the average of the y-cordinates of the vertices of T. If a certain triangle has vertices at the point (0,0)and (6,0) and centre at the point (3,2), what are the cordinates of the remainig vertex ?

1. (3,4)
2. (3,6)
3. (4,9)
4. (6,4)
5. (9,6)

1 (or A)

The mid-point is the average of the X vertices and the Y vertices.
Based on the given info, the baseline of the triangle has length = 6 and the mid-point has length = 3 and height 2, meaning the highest point should be 4.
Therefore, last unknown vertex should be (3,4) or A.
Manager
Joined: 23 Jan 2008
Posts: 108
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Re: any triangle T ? [#permalink]  04 Feb 2008, 17:56
misterJJ2u wrote:
Quote:
for any triangle T in the xy-cordinate plane, the centre of T is defined a to be the point whose x-cordinate is the average of the x-cordinate of the vertices of T and whose Y-cordinate is the average of the y-cordinates of the vertices of T. If a certain triangle has vertices at the point (0,0)and (6,0) and centre at the point (3,2), what are the cordinates of the remainig vertex ?

1. (3,4)
2. (3,6)
3. (4,9)
4. (6,4)
5. (9,6)

1 (or A)

The mid-point is the average of the X vertices and the Y vertices.
Based on the given info, the baseline of the triangle has length = 6 and the mid-point has length = 3 and height 2, meaning the highest point should be 4.
Therefore, last unknown vertex should be (3,4) or A.

answer is 2 . . .
Senior Manager
Joined: 20 Dec 2004
Posts: 257
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Kudos [?]: 84 [0], given: 0

Re: any triangle T ? [#permalink]  04 Feb 2008, 18:04
(0+6+x)/3 = 3 => x = 3

(0+0+y)/3 = 2 => y = 6.

(3,6) is the third vertex.

B.
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Re: any triangle T ?   [#permalink] 04 Feb 2008, 18:04
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