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 12 comma 0 labeled Obstacle 1, negative 12 comma 5 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. (3 points)
Part B: How many meters is one full lap around the course? Show every step of your work. (1 point)
Part A:
To find the distance from the starting point to obstacle 2, we can use the distance formula. The distance formula is given by the formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates for the starting point (x1, y1) are (-12, 5), and the coordinates for obstacle 2 (x2, y2) are (0, 0). Plugging these values into the distance formula, we get:
distance = √((0 - (-12))^2 + (0 - 5)^2)
= √((12)^2 + (-5)^2)
= √(144 + 25)
= √169
= 13 meters
Therefore, the distance from the starting point to obstacle 2 is 13 meters.
Part B:
One full lap around the course is the sum of the distances from the starting point to obstacle 1, from obstacle 1 to obstacle 2, and from obstacle 2 back to the starting point.
The distance from the starting point to obstacle 1 can be calculated using the distance formula:
distance1 = √((-12 - (-12))^2 + (0 - 5)^2)
= √((0)^2 + (-5)^2)
= √(0 + 25)
= √25
= 5 meters
The distance from obstacle 1 to obstacle 2 is simply the length of the shorter side of the right triangle, which is 12 meters.
The distance from obstacle 2 back to the starting point can be calculated using the distance formula again:
distance2 = √((0 - (-12))^2 + (0 - 5)^2)
= √((12)^2 + (-5)^2)
= √(144 + 25)
= √169
= 13 meters
Therefore, one full lap around the course is equal to:
distance = distance1 + distance2 + distance3
= 5 + 12 + 13
= 30 meters
Therefore, one full lap around the course is 30 meters.