AMC10 2012 B

AMC10 2012 B · Q3

AMC10 2012 B · Q3. It mainly tests Coordinate geometry, Transformations.

The point in the xy-plane with coordinates (1000, 2012) is reflected across the line y = 2000. What are the coordinates of the reflected point?

xy 平面上坐标为 (1000, 2012) 的点映关于直线 y = 2000。映点后的坐标是什么？

(A) (998, 2012) (998, 2012)

(B) (1000, 1988) (1000, 1988)

(D) (1000, 4012) (1000, 4012)

(E) (1012, 2012) (1012, 2012)

Answer

Correct choice: (B)

正确答案：（B）

Solution

The given point is 12 units above the horizontal line $y = 2000$. The reflected point will be 12 units below the line, and 24 units below the given point. The coordinates of the reflected point are (1000, 1988).

给定点在水平线 $y = 2000$ 上方 12 个单位。映点将在下方 12 个单位，即给定点下方 24 个单位。映点的坐标为 (1000, 1988)。

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