Question

jason and ronald
jason and ronald are camping at fortune island state park. a grid has been drawn to represent the locations of each of their campsites. each unit on the grid represents 100 feet.
if jason and ronald walk directly towards each other and meet halfway, how far, in feet, will each one need to walk? show the work you used to arrive at your answer. round your answer to the nearest foot.

Explanation:

Step1: Assign coordinates to camps

Let Jason's camp = $(1, 4)$, Ronald's camp = $(4, 1)$

Step2: Calculate total horizontal distance

$\Delta x = |4 - 1| = 3$ units

Step3: Calculate total vertical distance

$\Delta y = |1 - 4| = 3$ units

Step4: Find total straight-line distance

Use distance formula:
$$d = \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{3^2 + 3^2} = \sqrt{18} = 3\sqrt{2}$$

Step5: Find halfway distance

Half distance = $\frac{3\sqrt{2}}{2}$ units

Step6: Convert to feet (1 unit = 100 ft)

Distance in feet = $\frac{3\sqrt{2}}{2} \times 100 = 150\sqrt{2} \approx 212.13$

Step7: Round to nearest foot

Round $212.13$ to 212

Answer:

212 feet