+478 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.)
+1950 First, let's figure out the slope of the two points.
Since the slope is y2−y1x2−x1, the slope for (3,17) and (82,150) is
150−1782−3=13379
However, notice that between the two points, there are no lattice points.
This is because following the slope, after (3, 17), the next latice point is
(3+79,17+133)=(82,150)
Thus, the two endpoints are the only latice points, there are 2.
Thanks! :)
+1950 First, let's figure out the slope of the two points.
Since the slope is y2−y1x2−x1, the slope for (3,17) and (82,150) is
150−1782−3=13379
However, notice that between the two points, there are no lattice points.
This is because following the slope, after (3, 17), the next latice point is
(3+79,17+133)=(82,150)
Thus, the two endpoints are the only latice points, there are 2.
Thanks! :)
