1. **Stating the problem:** We have two points describing a mountain climbing expedition: Point A at (11,200 meters east, 3,200 meters above base camp) and Point B at (8,400 meters east, 1,700 meters higher than Camp A). We want to analyze the position and elevation difference between these points. 2. **Understanding the coordinates:** Point A's coordinates are given as $(x_A, y_A) = (11200, 3200)$ where $x$ is the eastward distance and $y$ is the elevation above base camp. 3. Point B's eastward position is $x_B = 8400$ meters east, and its elevation is $y_B = 3200 + 1700 = 4900$ meters above base camp. 4. **Calculate the horizontal distance between points A and B:** $$\text{Horizontal distance} = |x_A - x_B| = |11200 - 8400| = 2800 \text{ meters}$$ 5. **Calculate the vertical distance between points A and B:** $$\text{Vertical distance} = |y_B - y_A| = |4900 - 3200| = 1700 \text{ meters}$$ 6. **Calculate the straight-line distance (displacement) between points A and B using the Pythagorean theorem:** $$d = \sqrt{(x_A - x_B)^2 + (y_B - y_A)^2} = \sqrt{2800^2 + 1700^2}$$ 7. Calculate inside the square root: $$2800^2 = 7,840,000$$ $$1700^2 = 2,890,000$$ 8. Sum: $$7,840,000 + 2,890,000 = 10,730,000$$ 9. Take the square root: $$d = \sqrt{10,730,000} \approx 3276.5 \text{ meters}$$ 10. **Interpretation:** The straight-line distance between points A and B is approximately 3276.5 meters. This completes the analysis of the two points describing the mountain climbing expedition.