Math Problem Statement
Solve and show the graph illustration.
Solution
Here is the corrected graph representing the displacements for each row in the table. The blue vectors indicate the first and second moves, while the green vectors represent the resultant displacement for each case.
Would you like further clarification on any of the rows or the graph illustration? Here are some questions you may consider:
- How is displacement different from distance in vector problems?
- What is the significance of using the Pythagorean theorem for displacement?
- Why do some displacements have both magnitude and direction (e.g., Northeast, Southwest)?
- How would the graph change if you altered the direction of the movements?
- Can displacement ever be larger than the total distance?
Tip: Always remember, displacement is a vector quantity, meaning it has both magnitude and direction, whereas distance is a scalar (only magnitude).
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Math Problem Analysis
Mathematical Concepts
Vector Addition
Distance and Displacement
2D Motion
Formulas
Distance = Total path covered
Displacement = Final position relative to the starting point
Pythagorean Theorem: a^2 + b^2 = c^2 for calculating displacement in 2D
Theorems
Pythagorean Theorem for calculating displacement
Suitable Grade Level
Grades 8-10