In the x-y plane, point (x, y) is a lattice point if both x and y are integers. A rectangle has a center at (1, 2) and width (x), length (y), 6", 4", respectively. Some points, such as the center (1, 2), are inside the rectangle, but a point such as (4, 2) is on the rectangle, but not in the rectangle. How many lattice points are in the rectangle? Choose the correct choice:
A) 7
B) 71
C) 72
D) 17
E) 27
The lattice points that are in the rectangle can be calculated as follows: divide the rectangle into 4 quadrants. Now we solve for one quadrant, multiply by 4, and subtract the repeating points along the vertical and horizontal lines that lie along the center point.   For one quadrant we have:   vertical = (1, 2), (1, 3),   horizontal = (2, 2), (3, 2), (don't count center again),   others = (2, 2), (3, 3).   There are 6 points. So, 6 * 4 = 24. Subtract repeating points, 7, we get 17.   There are a total of 17 lattice points in the square.   Answer: 17
<result>D</result>
In the x-y plane, point (x, y) is a lattice point if both x and y are integers. A rectangle has a center at (1, 2) and width (x), length (y), 6", 4", respectively. Some points, such as the center (1, 2), are inside the rectangle, but a point such as (4, 2) is on the rectangle, but not in the rectangle. How many lattice points are in the rectangle?