Warm up
1. Find the distance
between the points
(1,4), and (-2, 3).
3.16
2. Find the distance
the ball was kicked
in the diagram.
50
(40,45)
(10,5)
(0,0)
Using Distance or
Pythagorean Theorem
Closest to the Origin
Ex: 1 Which point is closer to
the Origin, (-5, 2.1) or (6, 1)?
D
 5   2.1
2
D  5.42
2
D
6  1
2
2
D  6.08
(-5, 2.1) is closer to the Origin.
Ex: 2 Which point is closest to the
Origin, (1.5, -10), (12.2, 1) or (6.7, 7.7)?
D
1.5   10
2
2
D
12.2  1
2
2
D
6.7   7.7 
2
2
D  10.11 D  12.24 D  10.21
(-1.5, -10) is closest to the Origin.
Example 3
Which golf ball is closest to the hole?
10
8
6
4
2
-10 -8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
-10
Red (Q1) =5.39 Blue (QIV) = 5 Aqua(QIII) = 5.10
So the one in quadrant IV is the closest.
Example 4: If a circle is
centered at the origin and has a
radius of 5, where do these
points lie?
1.(3,4)
D= 5
On circle
2. (1, 5)
d = 5.1
outside circle
3. (2,3)
d=3.6
inside
Example 5: Does the point (-3,45)
lie on the circle centered at (-6,5) and containing the point
(15,-35)?
It lies outside
Homework
Using Coordinates to
Prove Theorems
#9B