Question

Diana left her campsite at (2, 9) on a map of Big Trees Park, hiked to Redwood Grove at (-9, 9), and

continued on to Bass Lake at (-9,-4). Each unit on the map represents 1 kilometer.
How far did Diana hike?

Answer 1

Diana hiked a total distance of 24 km from her campsite to Redwood Grove and then to Bass Lake.

Step-by-step explanation:

To find the distance Diana hiked, we need to calculate the distance between each pair of points she traveled to. We can use the distance formula, which is derived from the Pythagorean theorem, to find the distance between two points in a coordinate plane.

First, we find the distance between her campsite and Redwood Grove:
Distance = √((-9-2)^2 + (9-9)^2) = √((-11)^2 + 0^2) = √(121) = 11 km

Next, we find the distance between Redwood Grove and Bass Lake:
Distance = √((-9-(-9))^2 + (-4-9)^2) = √((0)^2 + (-13)^2) = √(169) = 13 km

Finally, we add the two distances together to find the total distance Diana hiked:
Total Distance = 11 km + 13 km = 24 km