9 1 Apply the Distance and Midpoint Formulas

9. 1 Apply the Distance and Midpoint Formulas Algebra II

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

The Distance Formula • The Distance d between the points (x 1, y 1) and (x 2, y 2) is :

1)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)

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

The Midpoint Formula • The midpoint between the two points (x 1, y 1) and (x 2, y 2) is:

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

Steps to write an equation in slope-intercept form for the perpendicular bisector of the segment • • • 1. ) Find the midpoint of segment 2. ) Find the slope of segment 3. ) Write the opposite & reciprocal slope. 4. ) Use either point-slope formula or slope intercept form (2)

4)Write an equation in slopeintercept 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.

(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

Assignment