1989 AHSME Problems/Problem 16
Problem
A lattice point is a point in the plane with integer coordinates. How many lattice points are on the line segment whose endpoints are (3,17) and (48,281)? (Include both endpoints of the segment in your count.)
Solution
Since the endpoints are (3,17) and (48,281), the line that passes through these 2 points has slope . The equation of the line passing through these points can then be given by . Since is reduced to lowest terms, in order for to be integral we must have that . Hence is 3 more than a multiple of 15. Note that corresponds to the endpoint . Then we have , , and where corresponds to the endpoint . Hence there are 4 in all.
See also
1989 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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