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12.8 The Distance Formula. CORD Math Mrs. Spitz Spring 2007. Objectives: Find the distance between two points in the coordinate plane, and 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

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12 8 the distance formula

12.8 The Distance Formula

CORD Math

Mrs. Spitz

Spring 2007


Objectives standard assignment

Objectives:

Find the distance between two points in the coordinate plane, and

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

Objectives/Standard/Assignment


Geometry review
Geometry Review!

  • What is the difference between the symbols AB and AB?

Segment AB

The length of Segment AB


The distance formula
The Distance Formula

  • The Distance d between the points (x1,y1) and (x2,y2) is :


Find the distance between the two points
Find the distance between the two points.

  • (-2,5) and (3,-1)

  • Let (x1,y1) = (-2,5) and (x2,y2) = (3,-1)


Classify the triangle using the distance formula as scalene isosceles or equilateral
Classify the Triangle using the distance formula (as scalene, isosceles or equilateral)

Because AB=BC the triangle is ISOSCELES


The midpoint formula
The Midpoint Formula scalene, isosceles or equilateral)

  • The midpoint between the two points (x1,y1) and (x2,y2) is:



Write an equation in slope-intercept form for the perpendicular bisector of the segment whose endpoints areC(-2,1) and D(1,4).

  • First, find the midpoint of CD.

    (-1/2, 5/2)

  • 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 perpendicular bisector of the segment whose endpoints are1)=m(x-x1) or y=mx+b

Use (x1 ,y1)=(-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


Assignment
Assignment perpendicular bisector of the segment whose endpoints are

  • WS 10.1 A and B (Yes I am borrowing from another text). WS B is extra credit for you.

  • Reminder: We have class 3 times this week.

  • Tuesday/Wednesday Chapter 12 Review

  • We will have a Test on Wednesday/Thursday before the long weekend. If you are slow, please come in during lunch sometime this week to finish. Thanks


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