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 (x1,y1) and (x2,y2) is :

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

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

1.) Find the midpoint of segment 2.) Find the slope of segment 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 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.

(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

Assignment