Notes #3 (1.3)Notes #3 (1.3)1-3 Distance and 1-3 Distance and

MidpointsMidpoints

Standard 17.0 Standard 17.0 Students prove Students prove theorems using coordinate theorems using coordinate geometry including the midpoint of geometry including the midpoint of a line segment, and the distance a line segment, and the distance formula midpoint formula midpoint

Objective: Objective: Find the distance Find the distance between two points and the between two points and the midpoint of a segment.midpoint of a segment.

Number LineNumber Line

The distance between P and Q is written PQ = |b – a| or |a – b|

a b

P Q

2)12(2)12( yyxxd

The distance d between two points (xThe distance d between two points (x11,y,y11) and ) and (x(x22,y,y22) is given by) is given by

The Distance FormulaThe Distance Formula

A(x1, y1)

B(x2, y2)

Midpoint Midpoint FormulasFormulas

The midpoint of a segment is the point on the The midpoint of a segment is the point on the segment that divides the segment into two segment that divides the segment into two congruent segmentscongruent segments

Number LineNumber Line Coordinate PlaneCoordinate Plane

2

,2

2121 yyxxM

2

baM

a and b are the endpoints x1, y1, x2, and y2 are coordinate points on the graph

ExampleExample

Find the coordinate of the midpoint of PQ, whereP is -20 and Q is 40

Find the coordinate of the midpoint of JK, whereJ(-1,2) and K(6, 1)

ExampleExample

Find the coordinates of the endpoint X if Y(-1,6) is the midpoint of XZ and Z (2,8)