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194. 想问则么做?则么求B点坐标阿?
In the rectangular coordinate system above, the line
y = x is the perpendicular bisector of segment AB (not
shown), and the x-axis is the perpendicular bisector of
segment BC (not shown). If the coordinates of point A
are (2,3), what are the coordinates of point C ?
(A) (–3,–2)
(B) (–3,2)
(C) (2,–3)
(D) (3,–2)
(E) (2,3)
Geometry Simple coordinate geometry
Since the line y = x is the perpendicular bisector
of AB , B is the reflection of A through this line.
In any reflection through the line y = x, the
x -coordinate and the y-coordinate of a point
become interchanged. Th us, if the coordinates of
A are (2,3), the coordinates of B are (3,2).
Since the x-axis is the perpendicular bisector of
BC , C is the reflection of B through the x-axis. In
any reflection through the x-axis, the x-coordinate
remains the same, and the sign of the y-coordinate
changes.
O
A y = x
y
x
3
2
1
–1
–2
1 2
B
C
Since the coordinates of B are (3,2), the
coordinates of C are therefore (3,–2).
Th e correct answer is D. |
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发表于 2011-8-10 10:58:12
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