Question

Jane wants to determine the shortest route from her home to her workplace. What is the distance of the shortest route from home to work to the nearest block?

a) 10 blocks

b) 8 blocks

c) 12 blocks

d) 15 blocks

Answer 1

Using the Pythagorean theorem, the shortest straight-line distance from Jane's home to her workplace is calculated to be approximately 10.3 blocks. This distance is rounded down to 10 blocks, making option (a) the correct answer.

Step-by-step explanation:

To determine the straight-line distance from Jane's home to her workplace, we need to calculate the hypotenuse of the resulting right triangle from her two-dimensional path. Jane walks a two-dimensional path that includes 9 blocks east and 5 blocks north, making a total of 14 blocks. To find the straight-line distance (hypotenuse), we use the Pythagorean theorem (a² + b² = c²), where the legs of the triangle (a and b) are 9 blocks and 5 blocks respectively.

The calculation would be: √(9 blocks)² + (5 blocks)² = √(81+25) = √106 ≈ 10.3 blocks. So, the shortest distance from home to work using the straight-line path is approximately 10.3 blocks, which we round down to 10 blocks to answer the original question.

Thus, the correct option for Jane's shortest route to her workplace to the nearest block is: a) 10 blocks.