The number of integral points (integral point means both the coordinates should be an integer) exactly in the interior of the triangle with vertices , and , is
Explanation of the correct option.
Step 1: Visually represent the given data.
Draw the given triangle and assume that, and .
Now, find the slope of the line as follows:
Since the slope of the line is which means that if we increase the value of by there is a decrease in the value of by .
Step 2: Find the number of required points.
We have to find the number of integral points exactly in the interior of the given triangle.
For .
The coordinates of that lie exactly inside the given triangle are .
So, the number of points that lie exactly inside the given triangle for is .
For .
The coordinates of that lie exactly inside the given triangle are .
So, the number of points that lie exactly inside the given triangle for is and so on.
And for .
The only point which lies inside the triangle is .
Find the total number of points that lie exactly inside the given triangle can be given by:
Therefore, the total number of points that lies exactly inside the given triangle is .
Hence, option is the correct option.