2. 外语
  3. Points A and B are shown in the xy-plane above. Point C(not shown)is above the x-axis so that the area of triangle ABC is 10. Wh

Points A and B are shown in the xy-plane above. Point C(not shown)is above the x-axis so that the area of triangle ABC is 10. Wh

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问题
Points A and B are shown in the xy-plane above. Point C(not shown)is above the x-axis so that the area of triangle ABC is 10. Which of the following could be the coordinates of C ?
Indicate all such coordinates.
选项 A、(0,4)
B、(1,3)
C、(2,5)
D、(3,4)
E、(4,5)
答案A，D
解析 From the figure, you can see that points A and B are on the x-axis. Since the x-coordinate of A is 1 and the x-coordinate of B is 6, the length of side AB is 5. Point C is not shown, but you know that C is above the x-axis and that the area of triangle ABC is 10. Using the formula for the area of a triangle, you can see that the height h from point C to the corresponding base AB satisfies the equation 10 =.
Therefore h = 4.
There are many possibilities for triangle ABC subject to these conditions. The following figures show three examples.

In the three examples, the dashed vertical line segments represent the height from point C to the base AB, and the coordinates of C are(3.5, 4),(5,4), and(8,4), respectively. Note that in all three cases, the y-coordinate of C is 4. In fact, for any triangle ABC that satisfies the conditions in the question, point C is a point with a y-coordinate of 4. Of the answer choices, only(0, 4)and(3, 4)have a y-coordinate of 4. The correct answer consists of Choices A and D.
This explanation uses the following strategies.
Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation
Strategy 6: Add to a Geometric Figure
Strategy 8: Search for a Mathematical Relationship
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