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Plane Problem

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Junior | Next Rank: 30 Posts
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by ssraf » Thu Jun 12, 2008 4:26 pm
For any point T in the xy-plane, the centre of T is defined to be the point whose x-coordinate is the average 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 triangle has vertices (0,0) and (6,0) and its centre at (3,2), what are the coordinates of the remaining vertice?

(3,4)
(3,6)
(4,9)
(6,4)
(9,6)

OA is B, shouldn't it be A????
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Re: Plane Problem

by Ian Stewart » Thu Jun 12, 2008 4:46 pm
ssraf wrote:For any point T in the xy-plane, the centre of T is defined to be the point whose x-coordinate is the average 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 triangle has vertices (0,0) and (6,0) and its centre at (3,2), what are the coordinates of the remaining vertice?

(3,4)
(3,6)
(4,9)
(6,4)
(9,6)

OA is B, shouldn't it be A????
The center, (3,2), is the average of the co-ordinates of the three vertices of the triangle, (0,0), (6,0), and some unknown point, let's say (c, d). So, averaging x-co-ordinates:

3 = (0+6+c)/3
9 = 6 + c
3 = c

and averaging y-co-ordinates

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

So the remaining vertex is (3, 6).
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