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A triangle is formed by the points (6,0),(0,0),(0,6).How many points with the integer coordinates are in the interior of the triangle?

A triangle is formed by the points (6,0),(0,0),(0,6).How many points with the integer coordinates are in the interior of the triangle?
 

Grade:10

3 Answers

Nishant
22 Points
6 years ago
 
 
 
Let me try a similar triangle: (0,0), (6,0), (0,6)
 
 
 
I assume that points on the side of the triangle are not "inside" it, so looking at each vertical line that is an integer value of x, I have x = 1, where the inside points go from y = 1 up to y = 4. We don't include y=5 because it is on the line itself, not inside.

The next value of x is x=2 where the possible integer values of y are y=1 up to y=3
So you can see that we can just add up the numbers:
           =  4 + 3 + 2 + 1=10
sachin
85 Points
6 years ago
 
I assume that points on the side of the triangle are not "inside" it, so looking at each vertical line that is an integer value of x, I have x = 1, where the inside points go from y = 1 up to y = 4. We don't include y=5 because it is on the line itself, not inside.

The next value of x is x=2 where the possible integer values of y are y=1 up to y=3
So you can see that we can just add up the numbers:
           =  4 + 3 + 2 + 1=10
sachin
85 Points
6 years ago
 
 assume that points on the side of the triangle are not "inside" it, so looking at each vertical line that is an integer value of x, I have x = 1, where the inside points go from y = 1 up to y = 4. We don't include y=5 because it is on the line itself, not inside.

The next value of x is x=2 where the possible integer values of y are y=1 up to y=3
So you can see that we can just add up the numbers:
           =  4 + 3 + 2 + 1=10

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