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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.)

 Jun 27, 2024

Best Answer 

 #1
avatar+14 
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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.

 Jun 27, 2024
 #1
avatar+14 
+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

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