2003 AMC 10B Problem 11

Attempt Problem 11 of the 2003 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 10B solutions, or check the answer key.

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11.

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?

2

5

7

12

20

Write each line in point-slope form through

(10, 15)

Set

y=0

in each equation to find where they cross the

x

-axis

The lines are

y-15=3(x-10)

and

y-15=5(x-10).

Setting

y=0

gives

x

-intercepts

x=5

and

x=7.

The distance between

(5,0)

and

(7,0)

2.

Thus, the correct answer is A.

Problem 11 in other years