1.3 midpoint and distance formulas

Mr. SaucedoGeometry

1.3 Midpoint and distance formula

ACTIVITY . SUPPLIES PER TEAM

1 PC OF LARGE CONSTRUCTION PAPER1 RULERPENCIL.1 PENNY (CAMERA)

ACTIVITY.A building in downtown Houston is looking for

a company to place surveillance cameras on several of its building walls. It will hire the company that can come up with the best way to place the camera in the exact center of the building wall.

VOCABULARY:MIDPOINT

DEFINITIONA point that divides the segment into two

congruent segments.VISUAL

LABELWe use two smallerLines to mark congruence.

VOCABULARYSEGMENT BISECTOR

DEFINITIONA point, ray, line, line segment or plane that

intersects the segment at its midpoint.

VISUAL

LABELUse the small marks toIndicate congruence.

GUIDED EXAMPLE 1Line l bisects AB at O.AO= 3.5, find AB.

GUIDED EXAMPLE 2Point O is the midpoint of AB.Find the length of AO if AO = 4x – 1 andOB = 3x + 3

MIDPOINT FORMULAIf you are given two points on a

coordinate plane, then the midpoint formula is:

Notice that you are basically taking the AVERAGE of the x-coordinates and the y-coordinates.

GUIDED EXAMPLE 3The endpoints of AB are A(1,2) and B(7,8). What are the coordinates of the midpoint of

AB?

GUIDED EXAMPLE 4The midpoint of VW is M(-1, -2). One

endpoint is W(4,4). Find the coordinates of endpoint V.

QUESTIONHow can we find the distance between

the two points?

QUESTIONHow can we find theDistance between points A and B?

THE DISTANCE FORMULA

THE DISTANCE FORMULA

GUIDED EXAMPLE 5What is the approximate length of

segment RS with endpoints R(3, 1) and S(-1, -5).

BIG QUESTIONSHow do you know thatPM = MR?

BIG QUESTION 2If I want to find the distance betweenPoints A and B. Does it matter which Point is used for (X1, Y1)?

INDEPENDENT PRACTICE

GEOMETRY BOOK, PAGE 19.

PROBLEMS: 1, 5, 8, 12, 14, 20, 22, 26, 32

PRE-AP add problems 2 & 47

HOMEWORK

WORKBOOK PAGES 7 & 8PROBLEMS: 2, 4, 5, 7, 8, 10, 12, 16, 18, 22,

24.

PRE-AP – add project to this homework. Due Mon. Sept. 9th.