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题库 / Prep2007E1-DS-213
If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?
(1) The coordinates of C are (a, 1 - b).
(2) The coordinates of D are (1 - a, b).
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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Coordinates of the midpoint M(xm,ym)M(xm,ym) of the line segment AB, (A(x1,y1)A(x1,y1) and B(x2,y2)B(x2,y2)) are xm=x1+x22xm=x1+x22 and ym=y1+y22ym=y1+y22
(1) C (a, 1 - b). Not sufficient.
(2) D (1 - a, b). Not sufficient.
(1)+(2) M(xm,ym)=M(x1+x22,y1+y22)=M(a+1−a2,1−b+b2)=M(12,12)M(xm,ym)=M(x1+x22,y1+y22)=M(a+1−a2,1−b+b2)=M(12,12). Sufficient.
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