Midpoint and Distance Formulas

DefinitionO The midpoint of a segment is the

point that divides the segment into two congruent segments.

Midpoint FormulaO The coordinates of the midpoint of a

segment are the averages of the x-coordinates and of the y-coordinates of the endpoints.

1 2 1 2,2 2

x x y yM

Finding a MidpointO Find the midpoint

between the endpoints (1, 7) & (3, -4).

O Find the midpoint between the endpoints (2, 5) & (-3, 9)

Finding an EndpointO If the midpoint of

segment AB is (2, 3) and A is at (-1, 5), where is B located?

O If the midpoint of segment CD is (0, -2) and D is at (3, 4), where is C located?

Distance FormulaO The distance formula is used to

compute the distance between two points in a coordinate plane. It is given by:

2 22 1 2 1( ) ( )d x x y y

Finding the DistanceO Find the distance between the points

(1, 4) and (-2, 8).

Partitioning a line segment in 1-dimension

A ratio of a:b means we are partitioning the segment into “a+b” parts1) find the length of the segment2) Multiply by the scaler “a/(a+b)”3) Add your answer to the first endpoint to determine the coordinate of the partition

Example:O The endpoints of segment PQ are -3

and 7. Find the coordinates of the point P that partitions the segment in the ratio 3:5

“Taxicab” Distance FormulaO Find the taxicab distance between (-

2, 8) & (1,4) by graphing.

Practice A2

WS