Question

Consider the square with vertices at (3, 3), (−3, 3), (−3, −3) and (3, −3). How many points with integer coordinates lie strictly in the interior of this square?

Answer 1

The number points with that lie strictly in the interior of the square are 25 points

Explanation:

The vertices of the square are; , (3, 3), (-3, 3), (-3, -3) and (3, -3)

From the attached diagram of the square created with Microsoft Word, where one box is equal to one unit, the number of points with integer coordinates that lie strictly in the interior of the square are given by the number of intersecting grid lines

The number of points on the interior of the square = 25 points

The points includes;

(-2, 2), (-1, 2), (0, 2), (1, 2), (2, 2)

(-2, 1), (-1, 1), (0, 1), (1, 1), (2, 1)

(-2, 0), (-1, 0), (0, 0), (1, 0), (2, 0)

(-2, -1), (-1, -1), (0, -1), (1, -1), (2, -1)

(-2, -2), (-1, -2), (0, -2), (1, -2), (2, -2).