AMC10 2009 B

AMC10 2009 B · Q12

AMC10 2009 B · Q12. It mainly tests Area & perimeter, Ratios in geometry.

Distinct points $A, B, C, D$ lie on a line, with $AB = BC = CD = 1$. Points $E$ and $F$ lie on a second line, parallel to the first, with $EF = 1$. A triangle with positive area has three of the six points as its vertices. How many possible values are there for the area of the triangle?

不同的点 $A, B, C, D$ 在一条直线上，且 $AB = BC = CD = 1$。点 $E$ 和 $F$ 在第二条与第一条平行的直线上，且 $EF = 1$。以六个点中的三个为顶点的三角形面积大于零。这样的三角形面积可能有几个不同的值？

(A) 3 3

(B) 4 4

(D) 6 6

(E) 7 7

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): The base of the triangle can be 1, 2, or 3, and its altitude is the distance between the two parallel lines, so there are three possible values for the area.

答案（A）：三角形的底边可以是 1、2 或 3，而它的高是两条平行线之间的距离，因此面积有三种可能的取值。

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