Final answer:
The distance between -13 and 13 on a number line is 26 units. For a two-dimensional path, the straight-line distance can be found using the Pythagorean Theorem, such as approximately 10.3 blocks for a walk of 9 blocks east and 5 blocks north. Displacements and distances are key concepts when dealing with vectors.
Step-by-step explanation:
The distance on a number line between -13 and 13 is calculated by finding the absolute difference between these two points. Since a number line is one-dimensional, we simply subtract the smaller number from the larger number (ignoring the sign) to find the distance. Therefore, the distance is 13 - (-13) which equals 26 units.
In the context of a two-dimensional path, such as walking 9 blocks east followed by 5 blocks north, we can use the Pythagorean Theorem to find the straight-line distance. Imagine this path forming a right triangle with legs of 9 blocks and 5 blocks. The straight-line distance would be the hypotenuse of this triangle. Applying the Pythagorean Theorem (a² + b² = c²), we find the straight-line distance to be √(9² + 5²) = √(81 + 25) = √106, which is approximately 10.3 blocks.
The concept of finding distances and displacements applies to problems involving vectors, as vectors have both magnitude and direction. For example, a displacement of 32 m to the right followed by 17 m to the left results in a net displacement of 15 m to the right, and the total distance traveled would be 49 m.