Difference between revisions of "2005 AMC 12A Problems/Problem 12"
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Revision as of 11:28, 31 July 2020
Problem
A line passes through and
. How many other points with integer coordinates are on the line and strictly between
and
?
Solution
For convenience’s sake, we can transform to the origin and
to
(this does not change the problem). The line
has the equation
. The coordinates are integers if
, so the values of
are
, with a total of
coordinates.
See also
2005 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 11 |
Followed by Problem 13 |
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.