Lesson 1-3:Use Distance and Midpoint

Formulas

Midpoints and Bisectors:

• The midpoint of a segment is the point that divides the segment into two congruent segments.

• A segment bisector is a point, ray, line, line segment, or plane that intersects the segment at its midpoint.

In the skateboard design, bisects at point T, and XT = 39.9 cm. Find XY.

VW XY

Line n bisects the segment. Find the indicated length.

n

A B C

Find AB if BC = 5/8 cm

n

D E F

Find DF if EF= 9 ½ m

n

A B C

Find AB if AC = 21 inches

Point M is the midpoint of . Find the length of . VM

VW

Identify the segment bisector of .

Then find PQ.

PQ

14

w

A M Cx + 20 5x - 4

Find AC

The Midpoint Formula:

If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the midpoint M of has coordinates

Midpoint (M) =

AB

1 2 1 2,2 2

x x y y

Ex: The endpoints of RS are R(1, -3) and S(4, 2). Find the coordinates of the midpoint M.

Ex: The endpoints of GH are G(7, -2) and H(-5, -6). Find the coordinates of the midpoint P.

Ex: The midpoint of JK is M(2, 1). One endpoint is J(1, 4). Find the coordinates of endpoint K.

Ex: The midpoint of AB is M(5, 8). One endpoint is A(2, -3). Find the coordinates of endpoint B.

Ex: The midpoint of AB is M(3, -4). One endpoint is A(-4, -6). Find the coordinates of endpoint B.

Distance Formula:

• To find the distance between two points, you will always use the Distance Formula.

• The Distance Formula:

If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the distance between A and B is

distance (d) = 2 2

2 1 2 1( ) ( )x x y y

Ex: What is the approximate length of RS with endpoints R(2, 3) and S(4, -1)? Round to the nearest tenth of a unit.

Ex: What is the approximate length of AB with endpoints A(-3, 2) and B(1, -4)? Round to the nearest tenth of a unit.

Find the length of the

segment. Round to the

nearest tenth of a unit.

The endpoints of two segments are given. Find each segment length. Tell whether the segments are congruent.

AB: A(-4, 0), K(4,8)

CD: C(-4, 2), D(3, -7)

Homework!

Pgs 19-21 #1, 3-20 all, 26-34 even, 43-45, 48, 49