+1000 How many lattice points (points with integer coordinates) are on the line segment whose endpoints are $(3,17)$ and $(82,150)?$ (Include both endpoints in your count.)
+1946 First, we must find the slope of the two points.
Since we have
\(\frac{150-17}{82-3} = \frac{133}{79}\)
This means for every 133 latice points to the right of 3, you move up 79.
However, note that when we add 133 to 17, we get \(133+17=150\)
This means there are no lattice points between \((3, 17), (82, 150)\)
So 2 is our answer.
Thanks! :)
