Transcript 1-4 Measuring Angles and Segments

Notes #3 (1.3)
1-3 Distance and Midpoints
Standard 17.0 Students prove
theorems using coordinate geometry
including the midpoint of a line
segment, and the distance formula
midpoint
Objective: Find the distance between
two points and the midpoint of a
segment.
Number Line
P
Q
a
b
The distance between P and Q is written
PQ = |b – a| or |a – b|
The Distance Formula

The distance d between two points (x1,y1) and (x2,y2)
is given by
B(x2, y2)
A(x1, y1)
d  ( x  x )2  ( y  y )2
2 1
2 1
Classwork #6
Pg. 25 (11-25)odd
Homework #6
Pg. 25 (12-28) even
Midpoint Formulas

The midpoint of a segment is the point on the segment
that divides the segment into two congruent segments
Number Line
a b
M
2
a and b are the endpoints
Coordinate Plane
M
 x1  x2 y1  y2 

 
,

2
2


x1, y1, x2, and y2 are
coordinate points on the graph
Example
Find the coordinate of
the midpoint of PQ, where
P is -20 and Q is 40
Find the coordinate of
the midpoint of JK, where
J(-1,2) and K(6, 1)
Example
Find the coordinates of the endpoint X if Y(-1,6) is
the midpoint of XZ and Z (2,8)
Classwork #7
Pg. 25 (5-10)
Homework #7
Pg. 27 (29-45) odd