Respuesta :
Answer:
The number of miles the homes of Fran's and Alex's homes are apart is approximately 8.602 miles
Step-by-step explanation:
The given displacements, d in vector form are;
For Fran;
3 miles west and 2 miles south gives d₁ = -3·i - 2·j
For Alex;
4 miles east and 3 miles north gives d₂ = 4·i + 3·j
The number of miles apart between Fran's and Alex's homes = d₂ - d₁
d₂ - d₁ = 4·i - (-3·i) + 3·j - (-2·j) = 7·i + 5·j
∴ The number of miles between Fran's and Alex's homes = 7·i + 5·j
The magnitude in miles in the distance between Fran's and Alex's homes = √(7² + 5²) = √74
∴ The magnitude in miles in the distance between Fran's and Alex's homes ≈ 8.602 miles
The magnitude in miles in the distance between Fran's and Alex's homes = The number of miles the homes of Fran's and Alex's homes are apart
∴ The number of miles the homes of Fran's and Alex's homes are apart ≈ 8.602 miles
