Question
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)
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)
Answers
GPT 3.5
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.
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.