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.)

Hi6942O Jul 9, 2024

#1**+1 **

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! :)

NotThatSmart Jul 9, 2024