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 (9,3) and center at the point (4,3), what are the coordinates of the remaining vertex?  Choose the correct answer:  A) (3,4)  B) (3,9)  C) (4,9)  D) (6,4)  E) (3,6)
Let (a,b) be the remaining vertex.   x: 0 + 9 + a = 3*4. Then a = 3.   y: 0 + 3 + b = 3*3. Then b = 6.   The answer is (3,6).
<result>E</result>
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 (9,3) and center at the point (4,3), what are the coordinates of the remaining vertex?