Final answer:
The straight-line distance in a right triangle can be calculated using the Pythagorean theorem, resulting in a hypotenuse length of 10.3 blocks, which is shorter than the 14 blocks walked.
Step-by-step explanation:
The student is asking for the straight-line distance between two points in a two-dimensional path where they have walked a total of 14 blocks. This scenario forms a right triangle, where one leg represents the distance going east (9 blocks), and the other leg represents the distance going north (5 blocks). To find the straight-line distance, which is the hypotenuse of the triangle, we use the Pythagorean theorem.
The Pythagorean theorem is represented by the equation A = ∙(Ax² + Ay²), where Ax and Ay are the lengths of the legs of the right triangle. In this case, Ax is 9 blocks and Ay is 5 blocks. Therefore, the straight-line distance A is calculated as:
A = √(9 blocks)² + (5 blocks)²
A = √(81 + 25)
A = √106
A = 10.3 blocks
The straight-line distance from the starting point to the destination is therefore 10.3 blocks. This distance is considerably shorter than the 14 blocks walked when following the two-dimensional path.