Maria is sailing her ship back to her home island but wants to stop at a neighboring island along the way, Maria knows her current location and the locations of both islands. How much shorter would it be for Maria to go straight home instead of making the additional stop?
Answers
Given : Maria is sailing her ship back to her home island but wants to stop at a neighboring island along the way, Maria knows her current location and the locations of both islands
To find : How much shorter would it be for Maria to go straight home instead of making the additional stop
Solution:
Let say Maria current Location = ( x₁ , y₁)
Home Island location = (x₃ , y₃)
Neighboring island Location = (x₂ . y₂)
How much shorter would it be for Maria to go straight home instead of making the additional stop
= Distance from current location to neighbor island + Distance from neighbor island to home island - Distance from current location to home island
Distance from current location to neighbor island = √(x₂ - x₁)² + (y₂ - y₁) ²
Distance from neighbor island to home island = √(x₃ - x₂)² + (y₃ - y₂) ²
Distance from current location to home island = √(x₃ - x₁)² + (y₃ - y₁) ²
= √(x₂ - x₁)² + (y₂ - y₁) ² + √(x₃ - x₂)² + (y₃ - y₂) ² - √(x₃ - x₁)² + (y₃ - y₁) ²
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