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