9.1 The Distance and Midpoint Formulas Algebra 2 Mrs. Spitz Spring 2007

Objectives/Standard/Assignment Objectives: 1.Find the distance between two points in the coordinate plane, and 2.Find the midpoint of a line segment in the coordinate plane. New Mexico Mathematics Performance Standards Grades 9–12: 2-E-1, 4-C-1 Assn: WS 10.1 A and B

Geometry Review! What is the difference between the symbols AB and AB?What is the difference between the symbols AB and AB? Segment AB The length of Segment AB

The Distance Formula The Distance d between the points (x 1,y 1 ) and (x 2,y 2 ) is :

Find the distance between the two points. (-2,5) and (3,-1) (-2,5) and (3,-1) Let (x 1,y 1 ) = (-2,5) and (x 2,y 2 ) = (3,- 1) Let (x 1,y 1 ) = (-2,5) and (x 2,y 2 ) = (3,- 1)

Classify the Triangle using the distance formula (as scalene, isosceles or equilateral) Because AB=BC the triangle is ISOSCELES

The Midpoint Formula The midpoint between the two points (x 1,y 1 ) and (x 2,y 2 ) is:The midpoint between the two points (x 1,y 1 ) and (x 2,y 2 ) is:

Find the midpoint of the segment whose endpoints are (6,-2) & (2,-9)

Write an equation in slope-intercept form for the perpendicular bisector of the segment whose endpoints are C(-2,1) and D(1,4). First, find the midpoint of CD.First, find the midpoint of CD. (-1/2, 5/2) Now, find the slope of CD.Now, find the slope of CD.m=1 * Since the line we want is perpendicular to the given segment, we will use the opposite reciprocal slope for our equation.

(y-y 1 )=m(x-x 1 ) or y=mx+b Use (x 1,y 1 )=(-1/2,5/2) and m=-1 (y-5/2)=-1(x+1/2) or 5/2=-1(-1/2)+b y-5/2=-x-1/2 or 5/2=1/2+b y=-x-1/2+5/2 or 5/2-1/2=b y=-x+2 or 2=b y=-x+2 y=-x+2

Assignment WS 10.1 A and B Reminder: We have class 3 times this week. We will have a quiz on Thursday before the long weekend.