Investigation distance & midpoint
stors to bryce canyon decided to hike on a trol. they stopped at the frst overlook and estimated that they hiked i womater
west and 2 klometers north.
many hikers reyon global positioning systems (gps) to determine location and distances: however, there are other methods
for determining how far you are from a set point, as you work on the folowing problems, look for answers to this question: what
information and calculations are needed to determine distance and location?
1. a coordinate grid can be used to determine how far the visitors are from where they started.
a. represent the distance and direction (1 km west and 2 km north) by drawing line
segments on a coordinate grid with the starting point at the origin. label the
coordinate point of the overlook where the visitors stopped.
b. draw a ine segment from the starting point to the overlook what shape does this
make
c. find the distance between the starting point and the overlook.
show/explain your work
2. the amazing amusement park is creating a new brochure. in the brochure, they want to include distances between some
of the most frequently visited attractions. use the copy of the map and the method from the problem above to find the
distances between each pair of attractions.
a. bumper cars and water slide
-roller counter
"acrobats
b. acrobats and arcade
do
concessions
arcade
c. ferris wheel and arcade
ferris wheet
-6 -6 -
3 - it
23
d. concessions and theater
theater
bumper car
?
water slide
e. roller coaster and acrobats
4
basketball shot
3. sarah is fred of drawing triangles and decides to look for a pattem to make finding distances more efficient. she notices
that she used the horizontal and vertical distance between two points for each right triangle she drew. she decides to
investigate a way to get these distances without always using a graph. follow sarah's thought process and her find a
poftem.
o. frst, she uses the coordinates of for the bumper cars and the water side since they are on the same horizontal ine. she
notices she could use the coordinates to her find the distance.
o what coordinates does she use? bumper cars (
o what distance does she find between the two?
) and water side _
_)
o how could she use coordinates, not the graph, to find the distance between the bumper cars and water slide?