A map of an obstacle course is shown in the graph. The running path for the course is shaped like a right triangle where each unit is equal to 1 meter.
graph of a right triangle with points at negative 6 comma 0 labeled Obstacle 1, negative 6 comma 8 labeled Starting Point, and 0 comma 0 labeled Obstacle 2
Part A: Find the distance in meters from the starting point to obstacle 2. Show every step of your work.
Part B: How many meters is one full lap around the course? Show every step of your work.
Part A: To find the distance from the starting point to obstacle 2, we can use the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and the y-coordinates.
The x-coordinate difference is 0 - (-6) = 6.
The y-coordinate difference is 0 - 0 = 0.
Plugging these values into the distance formula:
Distance = √(6^2 + 0^2)
= √(36 + 0)
= √36
= 6 meters.
Therefore, the distance from the starting point to obstacle 2 is 6 meters.
Part B: To find the distance for one full lap around the course, we need to calculate the distances between each point on the path.
The distance between obstacle 1 and the starting point is already given as 8 meters.
The distance from obstacle 1 to obstacle 2 can be found using the Pythagorean theorem since the path is a right triangle. The difference in the x-coordinates is 0 - (-6) = 6, and the difference in the y-coordinates is 0 - 0 = 0.
Using the Pythagorean theorem:
Distance = √(6^2 + 0^2)
= √(36 + 0)
= √36
= 6 meters.
The distance from obstacle 2 back to the starting point is the same as the distance from the starting point to obstacle 2, which is 6 meters.
Adding up the distances: 8 meters (obstacle 1 to starting point) + 6 meters (obstacle 1 to obstacle 2) + 6 meters (obstacle 2 to starting point) = 20 meters.
Therefore, one full lap around the course is 20 meters.