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12.8 The Distance Formula

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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

Assn: WS 10.1 A

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

Segment AB

The length of Segment AB

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

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

Because AB=BC the triangle is ISOSCELES

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

- 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-y1)=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

- 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