1. 10.1 The Distance and Midpoint Formulas What you should learn: Goal1 Goal2 Find the distance between two points and find the midpoint of the line segment joining two points. Classify a Triangle. 10.1 The Distance and Midpoint Formulas Goal3 Write an equation for a perpendicular bisector of a line segment.

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

3. The Distance Formula  The Distance d between the points (x 1,y 1 ) and (x 2,y 2 ) is : Goal1

4. A B C How long is a?4 How long is b?4 Pythagorean Formula: A 2 + b 2 = c 2 or c = √(a 2 +b 2 ) How long is c?5.7 A = x 2 – x 1 and B = y 2 –y 1

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

6. Classify the Triangle using the distance formula (as scalene, isosceles or equilateral) Because AB=BC the triangle is ISOSCELES Goal2

7. The Midpoint Formula  The midpoint between the two points (x 1,y 1 ) and (x 2,y 2 ) 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 m=1 * Since the line we want is perpendicular to the given segment, we will use the opposite reciprocal slope for our equation. Goal3

10. (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

11. Assignment