Coordinate Geometry Word Problems – Real-World Applications
Everything you've learned in this section – plotting points, reading coordinates, the distance formula, and the midpoint formula – comes together in real-world word problems. Maps, floor plans, sports fields, and delivery routes can all be modelled as coordinate grids, turning everyday questions like “how far apart are these two places?” or “where should we meet halfway?” into straightforward coordinate geometry calculations.
The key skill in word problems is translating the story into coordinates first, then applying the right formula – usually the distance formula or the midpoint formula from the main Coordinate Geometry page – exactly as you would with a purely numerical question.
Turning a Story into Coordinates
Read the word problem carefully to identify the coordinates involved, decide whether it's asking for a distance or a midpoint, then apply the matching formula.
Using the distance formula: d = √[(7−1)² + (10−2)²] = √[36 + 64] = √100 = 10 km.
Using the midpoint formula: M = ((0+8)/2, (0+6)/2) = (4, 3).
Real-Life Application
- Logistics: planning the shortest delivery route between two warehouses.
- Emergency services: choosing a central station location to minimise response distance.
- Event planning: picking a fair meeting point between multiple people's locations.
Key Takeaways
- Word problems become coordinate geometry once the story is translated into coordinates.
- “How far apart” questions use the distance formula.
- “Meet halfway” or “exact centre” questions use the midpoint formula.
Practice: Coordinate Geometry Word Problems
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