Final answer:
To find the displacement from John's home after moving 5 blocks south and 3 blocks west, we use the Pythagorean theorem and calculate the hypotenuse of the resulting right-angled triangle. The hypotenuse is approximately 5.83 blocks, so the nearest whole number is 6 blocks. Therefore, John is about 6 blocks away from his home.
Step-by-step explanation:
The question asks for the distance between John's starting point and his final position after moving 5 blocks south and 3 blocks west. This scenario can be visualized on a two-dimensional grid where John's movements create a right-angled triangle with the two sides measuring 5 blocks and 3 blocks. To find the distance from his home, also known as the displacement, we need to calculate the hypotenuse of this triangle.
Applying the Pythagorean theorem (a2 + b2 = c2), we have:
- Side a (south direction) = 5 blocks
- Side b (west direction) = 3 blocks
The hypotenuse (c), which is the straight-line distance, is calculated as follows:
c2 = a2 + b2
c2 = 52 + 32
c2 = 25 + 9
c2 = 34
c = √34
The square root of 34 is approximately 5.83, which we can round to the nearest whole number for the purpose of this question. Therefore, the closest answer would be 6 blocks, making option D correct.