Question: A centimetre square grid is shown below.
Point A has coordinates $(1, 3)$ and point B has coordinates $(9, 8)$.
Using Pythagoras' theorem, calculate the distance from $A$ to $B$. Give your answer to 1 d.p.
1. **State the problem:** We need to find the distance between points $A(1, 3)$ and $B(9, 8)$ on a coordinate grid.
2. **Formula:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by Pythagoras' theorem:
$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
3. **Calculate the differences:**
$$x_2 - x_1 = 9 - 1 = 8$$
$$y_2 - y_1 = 8 - 3 = 5$$
4. **Substitute into the formula:**
$$d = \sqrt{8^2 + 5^2} = \sqrt{64 + 25} = \sqrt{89}$$
5. **Evaluate the square root:**
$$d \approx 9.433...$$
6. **Round to 1 decimal place:**
$$d \approx 9.4$$
**Final answer:** The distance from $A$ to $B$ is approximately $9.4$ units.