Fran and Alex ride their bicycles from school. Fran rides 3 miles west and 2 miles south to get home. Alex rides 4 miles east and 3 miles north to get home. How many miles apart are Fran's and Alex's homes?

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

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