To solve this problem, Jason's movement creates a right triangle:

1. He walks 4 miles east.
2. Then he walks 6 miles north.
3. The direct path home represents the hypotenuse of this right triangle.

We can use the Pythagorean theorem: $c = \sqrt{a^2 + b^2}$ where:

• $a = 4$ miles,
• $b = 6$ miles,
• $c$ is the distance back home.

Calculation:

$c = \sqrt{4^2 + 6^2}$ $c = \sqrt{16 + 36} = \sqrt{52}$ $c \approx 7.2 \, \text{miles}.$

Final Answer:

The distance Jason walks to get home is 7.2 miles.

Answer: a. 7.2 miles

Would you like further clarification or details?
Here are 5 related questions for practice:

1. If Jason walked 8 miles north and 6 miles east instead, what would the distance back home be?
2. How can the Pythagorean theorem be applied to three-dimensional space?
3. If Jason’s path included an extra segment westward, how would we calculate the total distance?
4. What are some real-life applications of the Pythagorean theorem?
5. If Jason walked 5 miles east and 12 miles north, how far would he be from his house?

Tip: The Pythagorean theorem applies to any right triangle where the two legs and hypotenuse form a 90° angle.