The figure shows 4 points (A, B, C and D) in a square grid. Which of the following statements is false?

1. Determine the coordinates of each point from the grid description.

Let the bottom-left corner of the grid be $(0,0)$.

• Point A is at $(1, 2)$.
• Point B is at $(4, 5)$.
• Point C is at $(6, 3)$.
• Point D is at $(4, 1)$.

2. Evaluate statement (1): D is south of B.

B is at $(4, 5)$ and D is at $(4, 1)$. Since they have the same horizontal position and D is below B, D is exactly South of B. Statement (1) is true.

3. Evaluate statement (2): D is south-west of C.

C is at $(6, 3)$ and D is at $(4, 1)$. Moving from C to D requires going $2$ units West and $2$ units South. Since the horizontal and vertical distances are equal, D is exactly South-West of C. Statement (2) is true.

4. Evaluate statement (4): B is north-west of C.

C is at $(6, 3)$ and B is at $(4, 5)$. Moving from C to B requires going $2$ units West and $2$ units North. Since the horizontal and vertical distances are equal, B is exactly North-West of C. Statement (4) is true.

5. Evaluate statement (3): A is north-west of D.

D is at $(4, 1)$ and A is at $(1, 2)$. Moving from D to A requires going $3$ units West and $1$ unit North. Because the horizontal and vertical distances are not equal, A is not exactly North-West of D (it is West-North-West). Statement (3) is false.