a Notice that a circle centered at the origin with a radius of r passes through the points (r,0),(- r,0),(0,r) and (0,- r).
B
b Find the distance between the point and the origin using the Distance Formula.
A
a
B
b
Point
Zone
(3,4)
2
(6,5)
3
(1,2)
1
(0,3)
1
(1,6)
2
Practice makes perfect
a We are given a city's commuter has three zones, and are told that the first zone serves people that live within 3 miles of the city center. Let's draw a circle that represents the line between Zone 1 and Zone 2. This circle will be centered at the origin and will have a radius of 3.
Next we are given that the second zone serves people between 3 and 7 miles from the center and Sone 3 serves those over 7 miles. This means that the line between Zone 2 and Zone 3 can be represented by a circle centered at the origin that has a radius of 7.
Notice that a circle centered at the origin with a radius of r passes through the points (r,0),(- r,0),(0,r) and (0,- r).
b In this part we are asked to determine which zone serves people whose homes are represented by the given points.
(3,4), (6,5), (1,2), (0,3), (1,6)
First let's plot these points in our graph.
Looking at the graph, we can match the point with the zone. However we will also do this algebraically. Let's evaluate the distance between each point and the origin. Using this distance we will be able to determine in which zone the home is located.
Distance d
Zone
d≤ 3
1
3
2
d>7
3
Let's find the distances between the points and the origin using the Distance Formula. Then we will match each point with the zone using the above table.
