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Gary is taking Spot for a walk and travels from (-1, 9) to (2, 5) on a map. If each unit on the map is 2 km, how far did Gary and Spot walk?

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Final answer:

Gary and Spot walked a straight-line distance of 10 km between the points (-1, 9) and (2, 5) on the map, where each map unit represents 2 km in reality.

Step-by-step explanation:

To calculate the distance Gary and Spot walked between the points (-1, 9) and (2, 5) on the map, we will use the Pythagorean theorem because the walk forms a right-angled triangle between these two points. First, we find the horizontal and vertical distances they traveled. Horizontally, from -1 to 2 is 3 units, and vertically, from 9 to 5 is 4 units. On this map, each unit is equal to 2 km, so the actual distances are 6 km (3 units × 2 km/unit) and 8 km (4 units × 2 km/unit), respectively.

Now, to find the straight-line distance (hypotenuse) that Gary and Spot walked, we apply the Pythagorean theorem (a² + b² = c²):

  • a² = 6 km ² = 36 km²
  • b² = 8 km ² = 64 km²
  • c² = 36 km² + 64 km² = 100 km²
  • c = √100 km² = 10 km

Therefore, the straight-line distance Gary and Spot walked is 10 km.

User Rodrigo Siqueira
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