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Problem with a coordinate/statistic question

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Problem with a coordinate/statistic question

by hschwender » Tue Dec 29, 2009 8:50 am
Hi,

Today, I did a one of the practice tests from the official GMAT prep software and got the following question:

For any triangle T in the xy-coordinate plane, the center of T is defined to be the point whose x-coordinate is the average (mean) of the x-coordinates of the vertices of T and whose y-coordinates is the average (mean) 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)

I chose a) (3, 4), as for the x-coordinate (6+0) / 2 equals to 3 and for the y-coordinate (4+0) / 2 equals to 2. But the official answer is b.

Could someone help me?

Thanks
Heiko
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by papgust » Tue Dec 29, 2009 9:04 am
Average (mean) of vertices of a triangle is nothing but a centroid of a triangle.

If you recollect the formula for centroid = [(x1+x2+x3)/3, (y1+y2+y3)/3]

Here, you are given the centroid (3,2) and the other 2 vertices (x1,y1), (x2,y2). Now, find the third vertex (x3,y3).

centroid = [(x1+x2+x3)/3, (y1+y2+y3)/3]
(3,2) = [(0+6+x3)/3, (0+0+y3)/3]

Equate x and y co-ordinates separately,
3 = (0+6+x3)/3
x3 = 3

2 = (0+0+y3)/3
y3 = 6

Hence, (3,6)
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