The upper-left coordinates on a rectangle are $(-4,4)$, and the upper-right coordinates are $(4,4)$. The rectangle has an area of 8 square units.
Draw the rectangle on the coordinate plane below.
Answer
There will be 7 lattice positions between the two vertical sides of the rectangle, and there will be 0 lattice positions between the top and bottom of the rectangle. That's a total of \(7 \times 0 = \boxed{0}\) lattice points.
Step 1 ：The upper-left coordinates on a rectangle are \((-4,4)\), and the upper-right coordinates are \((4,4)\). This means the length of the rectangle is \(4 - (-4) = 8\) units.
Step 2 ：The rectangle has an area of 8 square units. Since the area of a rectangle is calculated by multiplying the length by the width, we can find the width by dividing the area by the length. So, the width of the rectangle is \(\frac{8}{8} = 1\) unit.
Step 3 ：The lower-left coordinates of the rectangle are \((-4,4-1) = (-4,3)\), and the lower-right coordinates are \((4,4-1) = (4,3)\).
Step 4 ：There will be 7 lattice positions between the two vertical sides of the rectangle, and there will be 0 lattice positions between the top and bottom of the rectangle. That's a total of \(7 \times 0 = \boxed{0}\) lattice points.
