A right-angled triangle ABC is shown on a grid. AB is along the x-axis and AC is along the y-axis. AB is 4 units and AC is 3 units. Calculate the length of the hypotenuse BC.

Step 1: Determine the lengths of the legs of the right-angled triangle $\triangle ABC$ from the diagram.
By counting the grid units and assuming 1 unit = 1 m:
The horizontal leg $\overline{AB}$ is 4 units long, so $\overline{AB} = 4 \text{ m}$.
The vertical leg $\overline{AC}$ is 3 units long, so $\overline{AC} = 3 \text{ m}$.

Step 2: Use the Pythagorean theorem to calculate the length of the hypotenuse $\overline{BC}$.

$$\overline{BC}^2 = \overline{AB}^2 + \overline{AC}^2$$ $$$$