Johnny starts his hike at his car site. He will take a break halfway between the car site and the campsite and then head on to the campsite. Use the diagram below to answer the questions.
(a graph of a coordinate plane. the max number for x is 13 and max number for y is 11. a dot that represents the car is on (2, 4) and the campsite is at (13, 7)
A. What are the coordinate’s of the rest stop?
B. How many units did Johnny travel to get to the campsite?
C. If each unit represents 3.5 meters, how many meters from the car to the campsite?
A. The rest stop is halfway between the car and the site, so use the midpoint formula.
B. Use the distance/length formula.
C. Multiply your answer from B. by 3.5.
To answer these questions, we can use the distance formula to calculate the distance between two points on a coordinate plane.
The distance formula is given by:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the answers to the questions step-by-step:
A. To find the coordinates of the rest stop, we need to find the midpoint between the car site and the campsite. The midpoint formula is given by:
midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Plugging in the coordinates of the car site (2, 4) and the campsite (13, 7) into the midpoint formula, we get:
midpoint = ((2 + 13) / 2, (4 + 7) / 2)
= (15 / 2, 11 / 2)
= (7.5, 5.5)
Therefore, the coordinates of the rest stop are (7.5, 5.5).
B. To find the distance Johnny traveled to get to the campsite, we need to calculate the distance between the car site and the campsite using the distance formula.
Plugging in the coordinates of the car site (2, 4) and the campsite (13, 7) into the distance formula, we get:
distance = sqrt((13 - 2)^2 + (7 - 4)^2)
= sqrt(11^2 + 3^2)
= sqrt(121 + 9)
= sqrt(130)
≈ 11.4 units
Therefore, Johnny traveled approximately 11.4 units to get to the campsite.
C. Since each unit represents 3.5 meters, we can find the distance in meters by multiplying the number of units by 3.5.
Plugging in the distance in units (11.4) into the conversion factor, we get:
distance in meters = 11.4 * 3.5
≈ 39.9 meters
Therefore, the distance from the car site to the campsite is approximately 39.9 meters.