1. **State the problem:** A young green sea turtle moves south 3.2 cm and east 5.1 cm on a map where 1 cm equals 6 km. We need to find the turtle's displacement, which is the straight-line distance from start to finish. 2. **Formula used:** We use the Pythagorean Theorem for right triangles: $$c = \sqrt{a^2 + b^2}$$ where $a$ and $b$ are the legs and $c$ is the hypotenuse (displacement). 3. **Convert distances to kilometers:** $$a = 3.2 \text{ cm} \times 6 = 19.2 \text{ km}$$ $$b = 5.1 \text{ cm} \times 6 = 30.6 \text{ km}$$ 4. **Calculate displacement:** $$c = \sqrt{19.2^2 + 30.6^2} = \sqrt{368.64 + 936.36} = \sqrt{1305}$$ 5. **Simplify:** $$c = \sqrt{1305} \approx 36.12 \text{ km}$$ 6. **Answer:** The turtle's displacement is approximately **36.12 km**.