a Lattice point has integer coordinates
An ant walks directly from (0,0) to (24, 18). How many lattice points does it walk through while traveling?
To find the number of lattice points the ant walks through, we can use the formula for the number of lattice points on a line segment between two points (x1, y1) and (x2, y2). The formula is given by:
Number of lattice points = gcd(|x2 - x1|, |y2 - y1|) + 1
In this case, the ant walks from (0, 0) to (24, 18), so x1 = 0, y1 = 0, x2 = 24, and y2 = 18.
Number of lattice points = gcd(|24 - 0|, |18 - 0|) + 1
= gcd(24, 18) + 1
= 6 + 1
= 7
So, the ant walks through 7 lattice points while traveling from (0, 0) to (24, 18).