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.)

bingboy Jun 27, 2024

#1**+1 **

The slope of the line is \(\frac{150-17}{82-3} = \frac{133}{79}\) .(This cannot be further simplified). Starting from point \((3,17)\), the next point with integer coords will be \((82, 150)\), which is the second endpoint. So there are only \(\boxed{2}\) lattice points in the line, that being the two endpoints.

AsianMathGuy Jun 27, 2024

#1**+1 **

Best Answer

The slope of the line is \(\frac{150-17}{82-3} = \frac{133}{79}\) .(This cannot be further simplified). Starting from point \((3,17)\), the next point with integer coords will be \((82, 150)\), which is the second endpoint. So there are only \(\boxed{2}\) lattice points in the line, that being the two endpoints.

AsianMathGuy Jun 27, 2024