2018 AMC 12B Problems/Problem 3
Contents
Problem
A line with slope intersects a line with slope at the point . What is the distance between the -intercepts of these two lines?
Solution 1
Using point slope form, we get the equations and . Simplifying, we get and . Letting in both equations and solving for gives the -intercepts: and , respectively. Thus the distance between them is .
Solution 2
In order for the line with slope to travel "up" units (from ), it must have traveled units to the right. Thus, the -intercept is at . As for the line with slope , in order for it to travel "up" units it must have traveled units to the right. Thus its -intercept is at . Then the distance between them is .
See Also
2018 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 2 |
Followed by Problem 4 |
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All AMC 12 Problems and Solutions |
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