Let’s break down the information provided in the problem:
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Distance and Displacement: The total distance run (from Point B to Point A, from A to D, and from D to C) is \( m \). The total displacement (the straight-line distance from Point B to Point C) is \( m \) East.
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Distance Relationships:
- The distance from Point B to Point A is \( b \).
- The distance from Point A to Point D is \( b - 4 \) (from the equation \( b - a = 4 \)).
- The distance from Point D to Point C is \( 4 \).
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Distances:
- From the notation, if \( b \) is the distance from B to A, we have:
- Distance from Point B to A: \( b \)
- Distance from Point A to D: \( b - 4 \)
- Distance from Point D to C: \( 4 \)
- From the notation, if \( b \) is the distance from B to A, we have:
Let's find the total distance based on this information:
\[ \text{Total Distance} = \text{BA} + \text{AD} + \text{DC} \]
Substituting the distances into the equation: \[ \text{Total Distance} = b + (b - 4) + 4 \] \[ = b + b - 4 + 4 \] \[ = 2b \]
Since we know the total distance is \( m \): \[ 2b = m \]
From this, we can derive that: \[ b = \frac{m}{2} \]
- Displacement: Since the total displacement is \( m \) East, we can associate the directions with the points defined. The runner's movement creates a resultant vector from Point B to Point C. By considering the distances traveled and their respective directions, we will find that the distance from Point C to Point B equals \( m \) in the East direction.
To summarize:
- \( b = \frac{m}{2} \) (this is the distance BA).
- The other points indicate specific traveled distances.
- We conclude that \( a, c, \) and \( d \) can be defined but might be difficult to connect without further definitions on their locations in relation to each other (e.g., where exactly A, D, and C are in terms of a coordinate system).
If you have any more specific questions or need clarification on any part, feel free to ask!