Question - Determining Distance to Dog Park
Solution:
The image provides a word problem about James and Amber who walk their dogs together at a nearby dog park. They wish to determine who has to walk a farther distance to get to the dog park. The question requires the use of a coordinate plane to determine the distances, with the town square (origin) at (0,0), James's house at (1, -4), Amber's house at (2, -6), and the dog park at (2, 4).To find out how far each person lives from the dog park, you need to calculate the distance between their houses and the dog park using the distance formula for coordinates:Distance = √((x2 - x1)² + (y2 - y1)²)For James:Distance between James's house and the dog park = √((2 - 1)² + (4 - (-4))²) = √((1)² + (8)²) = √(1 + 64) = √(65)For Amber:Distance between Amber's house and the dog park = √((2 - 2)² + (4 - (-6))²) = √((0)² + (10)²) = √(0 + 100) = √(100) = 10Comparing the two distances, √(65) is less than 10, which means James lives closer to the dog park than Amber.The statement to complete would therefore be:James is √(65) blocks from the dog park and Amber is 10 blocks from the dog park. This means that Amber is farther from the dog park.
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