a Lattice point has integer coordinates

Question

An ant walks directly from (0,0) to (24, 18). How many lattice points does it walk through while traveling?

Answer 1

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).