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avatar+713 

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.)

 Jul 9, 2024
 #1
avatar+1271 
+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! :)

 Jul 9, 2024
 #2
avatar+57 
0

Or 133 and 79 are relatively prime, so 2

 Jul 10, 2024

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