midpoint section: 1.7 sol:g.3a midpoint is a point in a line segment that splits the line into two...
TRANSCRIPT
MidpointSection: 1.7Sol:G.3a
Midpoint
Is a point in a line segment that splits the line into two congruent segments.
Therefore, AX=XB
A
Midpoint
BX
Segment Bisector
Is a segment bisector of
A BM
is a point, ray, line, line segment or plane that intersects a segment as a midpoint.
D
C
CDAB
MBAM Therefore,
and
MBAM
Ex:
In the skateboard design, BISECTS at point T, and find .
VW XY
cmXT 39 XY
X 39.9
T
YW
V
TYXT TYXTXY
9.399.39 XYcmXY 8.79
Using Algebra with line segments
Point M is the midpoint of ; Find the length of .
V WM
VWVW
4x - 1 3x + 3
The Midpoint Formula•The coordinates of a segment are the
averages of the x-coordinates and of the y-coordinates of the endpoints.
• If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the midpoint M of AB has coordinates:
•Diagram on overhead.
2,
22121 yyxx
Example:
Find the Midpoint if the endpoints of are
R(1, -3) and S(4, 2).
RS
Try This
Find the Midpoint(M) of if the endpoints are
A(1,2) and B(7, 8)
AB
Example: place a point on the graph.
Given a parallelogramwith vertices A(5, 3),B(2, 3), C(-5, -7), and D(-2, -7). At what point will the diagonals of the parallelogram intersect?
Ex: Finding the missing endpointFind the coordinates of the missing
endpoint of when M(2,1) and one endpoint is J(1,4).
Find the coordinates of K.
JK
Try this:
Find the coordinates of the missing endpoint of
when M(-1,-2) and one endpoint is W(4,4). Find the coordinates of V.
VW
Assignments
Classwork: WB PG 27 1-16, 26
Homework: Pg 53-55 1,2,6-20even