1. 1-3 The Distance and Midpoint Formulas
Geometry

2. Objectives: Objectives:
Find the distance between two points in the coordinate plane, and
Find the midpoint of a line segment in the coordinate plane.

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