Difference between revisions of "2018 AMC 12B Problems/Problem 3"
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== Problem == | == Problem == | ||
| − | A line with slope 2 intersects a line with slope 6 at the point <math>(40,30)</math>. What is the distance between the <math>x</math>-intercepts of these two lines? | + | A line with slope <math>2</math> intersects a line with slope <math>6</math> at the point <math>(40,30)</math>. What is the distance between the <math>x</math>-intercepts of these two lines? |
| − | <math> | + | <math>\textbf{(A) } 5 \qquad \textbf{(B) } 10 \qquad \textbf{(C) } 20 \qquad \textbf{(D) } 25 \qquad \textbf{(E) } 50</math> |
== Solutions == | == Solutions == | ||
Revision as of 04:47, 18 September 2021
Problem
A line with slope 
intersects a line with slope 
at the point 
. What is the distance between the 
-intercepts of these two lines?
Solutions
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 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
