1958 AMC 12 第 27 题

Question

点

(2,-3)

、

(4,3)

和

(5,\frac{k}{2})

在同一直线上。

k

的值为：

The points

(2,-3),

(4,3),

and

(5,\frac{k}{2})

are on the same straight line. The value(s) of

k

is (are):

12

-12

\pm12

12

或

6

12

or

6

6

或

6\frac23

6

or

6\frac23

计算经过前两个点的直线斜率

Compute the slope through the first two points

令该斜率等于从

(4,3)

到

(5,\frac{k}{2})

的斜率

Equate that slope to the slope from

(4,3)

to

(5,\frac{k}{2})

经过前两个点的直线斜率为

\frac{3-(-3)}{4-2}=3\text{。}

因此

\frac{\frac{k}{2}-3}{5-4}=3\text{，}

得到

\frac{k}{2}=6

和

k=12

。

所以正确答案为 A。

The slope through the first two points is

\frac{3-(-3)}{4-2}=3.

Thus

\frac{\frac{k}{2}-3}{5-4}=3,

which gives

\frac{k}{2}=6

and

k=12.

Therefore, the correct answer is A.

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