Final answer:
The statement regarding the Pythagorean theorem and vector components forming a right-angle triangle is true. The statement about wave amplitudes affecting each other is also true. The claim about one person having more displacement than the other given the same start and end points is false; their displacements would be the same.
Step-by-step explanation:
The given statements pertain to various mathematical concepts, including geometry, vectors, and displacement. Let's analyze each one:
- Pythagorean theorem can indeed be used to calculate the length of the resultant vector when two vectors are at right angles to each other. Therefore, the statement is True.
- A vector can be broken down into x and y components that form the shape of a right-angle triangle, hence the statement is True.
- The amplitude of one wave is affected by the amplitude of another wave when they are in phase or precisely aligned. This scenario describes constructive or destructive interference, so the statement is True.
- The displacement of a person walking 2 blocks east and 5 blocks north will be the same as another person walking 5 blocks north and then 2 blocks east because displacement depends only on the initial and final position, not the path taken. Thus, the statement is False. The corrected statement would be: 'The displacement of the first person will be the same as the displacement of the second person.'