Algebra 2
Chapter 9 Conic Sections: Circles and
Parabolas
9-1 Distance and Midpoint Formulas
 WARMUP:
 Simplify:
1. -5 + 2
2. ( -1 – (-4))2
3. | -2 + (-6) |
4. (3 – (-5))2 – ( -4 - 2)2
5.
7  (3)
2
9-1 Distance and Midpoint Formulas
 Objective: To find the distance between any
two points and the midpoint of the line
segment joining them.
9-1 Distance and Midpoint Formulas
 Chapter 9 has a subtitle of “Conic
Sections”.
 http://clem.mscd.edu/~talmanl/HTML/ConicS
ections.html
9-1 Distance and Midpoint Formulas
 How do we tell the distance between any
two points on a number line?
9-1 Distance and Midpoint Formulas
 The distance between any two points P and
Q is written PQ. On a number line, PQ is
the absolute value of the difference between
their coordinates.
 Since | a – b | = | b – a | order doesn’t
matter.
 Example:
9-1 Distance and Midpoint Formulas
 What about two points in a coordinate
plane?
 Pick two points…
9-1 Distance and Midpoint Formulas
 Reminder:
Pythagorean Theorem:
If the length of the hypotenuse of a right triangle
is c, and the lengths of the other two sides
(legs) are a and b, then
c  a b
2
2
2
9-1 Distance and Midpoint Formulas
Distance between
P1 ( x1 , y1 ) and
P2 ( x2 , y2 ) is?
9-1 Distance and Midpoint Formulas
 The Distance Formula:
The distance between the points P1 ( x1 , y1 )
and P2 ( x2 , y2 ) is:
PP
1 2  ( x2  x1 )  ( y2  y1 )
2
2
9-1 Distance and Midpoint Formulas
 Find the distance between:
1. points: ( -2, -1 ) and ( -4, 3 )
2. points: ( 2, -7 ) and ( 2, -1 )
9-1 Distance and Midpoint Formulas
 The distance formula can be used to prove
the Midpoint Formula:
 The Midpoint Formula:
The midpoint (M) of the line segment joining
P1 ( x1 , y1 ) and P2 ( x2 , y2 ) is
 x1  x2 y1  y2 
M
,

2 
 2
9-1 Distance and Midpoint Formulas
 Find the midpoint of the line segment joining
the points:
1. ( 4, -6 ) and ( -3, 2 )
2. ( 7, 5 ) and ( -1, -3 )
9-1 Distance and Midpoint Formulas
 Typical test question:
 Find the coordinates of Q given that M is the
midpoint of the line segment PQ:
P( 0, 0 ), M( 3, 5 )
Can do it graphically. On a test you MUST do it
mathematically…
9-1 Distance and Midpoint Formulas
9-1 Distance and Midpoint Formulas
 More examples:
9-1 Distance and Midpoint Formulas
 Homework: