2003 AMC 10B Problem 11

Problem 11 of 25IntermediateAlgebra 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?

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Solution

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.

Concepts: coordinate geometry · slope · linear equation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.