1-3 The Distance and Midpoint Formulas

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Presentation transcript:

1-3 The Distance and Midpoint Formulas Geometry

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

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 :

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

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:

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

(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