AMC10 2003 B
AMC10 2003 B · Q11
AMC10 2003 B · Q11. It mainly tests Linear equations, Coordinate geometry.
A line with slope 3 intersects a line with slope 5 at the point (10, 15). What is the distance between the x-intercepts of these two lines?
一条斜率为 3 的直线与一条斜率为 5 的直线相交于点 (10, 15)。这两条直线的 x 轴截距之间的距离是多少？
(A)
2
2
(B)
5
5
(C)
7
7
(D)
12
12
(E)
20
20
Answer
Correct choice: (A)
正确答案：（A）
Solution
(A) The two lines have equations
$y-15=3(x-10)$ and $y-15=5(x-10)$.
The $x$-intercepts, obtained by setting $y=0$ in the respective equations, are 5 and 7. The distance between the points $(5,0)$ and $(7,0)$ is 2.
（A）两条直线的方程为
$y-15=3(x-10)$ 和 $y-15=5(x-10)$。
将各自方程中的 $y=0$，得到 $x$ 轴截距分别为 5 和 7。点 $(5,0)$ 与 $(7,0)$ 之间的距离为 2。
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