2. 外语
  3. In the rectangular coordinate system above, if P, not shown, is a point on AB and if the x-coordinate of P is 1, what is the y-c

In the rectangular coordinate system above, if P, not shown, is a point on AB and if the x-coordinate of P is 1, what is the y-c

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问题
In the rectangular coordinate system above, if P, not shown, is a point on AB and if the x-coordinate of P is 1, what is the y-coordinate of P?
选项 A、4/3
B、3/2
C、7/3
D、5/2
E、8/3
答案A
解析 上图所示的直角坐标系中，若P(未标出)是AB上一点，且P的横坐标为1，那么P的纵坐标为多少?
解：本题的正确答案为(A)。先写出直线AB的方程，然后把P点的坐标代入即可：y/2 + x/3 =1或y=-2/3 x +2。由此方程可得当x=1时，y=4/3。若考生对直线方程不太熟悉，则可以借助相似三角形的性质来解此题。显然由虚线切出的小三角形与△ABO相似，由此可推出y/2=(3-1)/3→ y=4/3
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