Question

A caterpillar crawling in a straight line across a coordinate plane starts at point (-3,

-4) and ends at point (25, 38). Counting the start point and end point, how many
points with integer coordinates does the caterpillar touch?

Answer 1

9514 1404 393

Answer:

15

Explanation:

In vector form, the equation of point p on the line can be written as ...

p = (-3, -4) +t(25 -(-3), 38 -(-4)) . . . . . for some scalar t

p = (-3, -4) +t(28, 42)

p = (-3, -4) +14t(2, 3)

where t takes on any value between 0 and 1.

If we let t = n/14 for some integer 0 ≤ n ≤ 14, then the coordinates of point p will be integers.

There are 15 values that n can have in the allowed range.

The caterpillar touches 15 points with integer coordinates.