Sections 9-2 CiRcLeS

1
ALGEBRA II HONORS _at_
THE DISTANCE and MIDPOINT FORMULAS
2
Golf Cart Gallivanting
Gertrude Gilmore lives in The Villages, a lovely
retirement community in sunny south Florida!
Gertrude spends her Saturdays driving her golf
cart around their small town to get groceries, go
to lunch, then to the gym, and finally to get her
hair done before she plays horse shoes and
shuffle board on Saturday nights in the town
square. Gertrude is on her final two activities
before her big night out with her friends. She
has to get from the gym to the hair salon in the
shortest distance and in the shortest amount of
time. She has just enough time to get from the
gym to the salon, but only if it is XX miles
away. Will she be able to make it? Lets
find out!
3
Golf Cart Gallivanting
SALON
Gym (G) ( 2 , 3 ) Salon (S) ( 10 , 9 ) Park
(P) ( _____ , _____ )

PARK
GYM
4
Golf Cart Gallivanting using a right triangle

What are the coordinates for the Park? Park
(P) ( ? , ? )
S (10 , 9)
c
b
G (2, 3)
P ( 10 , 3 )
a
5
DISTANCE FORMULA

• a2 b2 c2 Pythagorean Theorem
• (GP)2 (PS)2 (GS)2 Pythagorean
  Theorem with substitutions
• (x2-x1)2 (y2-y1)2 (d)2 Substitute into
  standard form using given
  variables
• Equation for the distance
  between two points

6
Gertrudes Detour
SALON
Gertrude stops on the way from the gym to the
salon to grab a new pair of red high heels to
wear to the games tonight. She stops exactly half
way between the two places, what is the location
of the store where she stopped to buy her shoes?
STORE
PARK
GYM
7
What about the midpoint of line segment GS?

S (x2 , y2)
M
G (x1, y1)
P (x2 , y1)
8
Midpoint Formula
What we need is the midpoint of the line segment
GS, but its only half the length, not the whole
length.
9
EXAMPLES

• Find the distance between the two points, and the
  midpoint of the line segment they create.
• (4,6) and (1, 9)
• (6,-7) and (-3,5)

10

• 3) (-7, -2) and (14 , -2)

11
What if we were given one endpoint and the
midpoint of a line segment? How would we find
the other endpoint?

• 7) Endpoint (-9,1) Midpoint (8, 14)
• 8) Endpoint (11,14) Midpoint (10,14)

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