1. The Distance and Midpoint Formulas

2. Objectives/Assignment
Find the distance between two points and find the midpoint of the line segment joining two points.
Use the distance and midpoint formulas.
Assignment: odd

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

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

5. Find the distance between the two points.
(-2,5) and (3,-1)
Let (x1,y1) = (-2,5) and (x2,y2) = (3,-1)

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

7. The Midpoint Formula
The midpoint between the two points (x1,y1) and (x2,y2) is:

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

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.
(-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.

10. (y-y1)=m(x-x1) or y=mx+b (y-5/2)=-1(x+1/2) or 5/2=-1(-1/2)+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