Question

Logan plans to run in the annual Fun Run. The route for the run is shown on the graph. Race participants run along a grid of streets from the starting point to points A, B, C, and then the finish line. Each unit on the grid represents 1 block. y x A Start 1 22 242 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 21 22 23 24 25 B CFinish Fun Run Route Part A What is the total distance of the race? Enter your work or explanation in the box provided.

Answer 1

To calculate the total distance of the race Logan will run from the starting point to points A, B, C, and then to the finish line, we need to determine the distances from each point to the next along the grid.

Assume the starting point is at coordinates (x1, y1) on a grid defined as a coordinate system:

1. **Starting Point to A:**
- If the coordinates of point A are (x_A, y_A), the distance from the start to A can be calculated using the formula for Manhattan distance (since movement is restricted to a grid):
\[
\text{Distance} = |x_A - x1| + |y_A - y1|
\]

2. **A to B:**
- Similarly, if B is at (x_B, y_B):
\[
\text{Distance from A to B} = |x_B - x_A| + |y_B - y_A|
\]

3. **B to C:**
- For point C at (x_C, y_C):
\[
\text{Distance from B to C} = |x_C - x_B| + |y_C - y_B|
\]

4. **C to Finish:**
- And if the Finish line is at (x_F, y_F):
\[
\text{Distance from C to Finish} = |x_F - x_C| + |y_F - y_C|
\]

5. **Total Distance:**
- We then add up all the distances calculated:
\[
\text{Total Distance} = \text{(Start to A)} + \text{(A to B)} + \text{(B to C)} + \text{(C to Finish)}
\]

**Note:** Without the actual coordinates for points A, B, C, and the finish line from the graph, we can't compute the specific numerical values. You would need to provide the coordinates or the graph data for more precise calculations.

Once the distances are calculated using the above formulas, just add them together to find the total distance of the race.