AMC 8 1996 Problem 17
AMC8 1996 年第 17 题
坐标几何★★★☆☆
Figure is a square. Point is the origin, and point has coordinates (2,2). What are the coordinates for so that the area of triangle equals the area of square ?
NOT TO SCALE
图形 是一个正方形。点 是原点，点 的坐标为 (2,2)。点 的坐标应为何值，才能使三角形 的面积等于正方形 的面积？
（图形未按比例绘制）
- A.(-6,0)
- B.(-4,0)
- C.(-2,0)
- D.(2,0)
- E.(4,0)
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
The area of is .
The area of is .
If we set the areas equal, the area of is 4. Also, note that PQ=2. Plugging those in, we get:
, PT = 4
If PT = 4, and PO = 2, then OT = 2, and must be 2 units to the left of the origin. This would be (-2,0), giving answer .
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