Midpoint and Distance Formulas

Section 1.3

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).

Alternative to the Distance Formula

O The distance formula comes from the Pythagorean theorem: a2 + b2 = c2

O If you are unsure about the distance formula, graph the two points accurately on a graph and use the Pythagorean theorem to find the distance.

Finding distanceO Find the distance between (-2, 3) &

(10, 8) by graphing and using the Pythagorean theorem.

Compare the two waysO Find the distance

between (-7, -3) & (8, 5) using the distance formula.

O Graph the same two points and find the distance using the Pythagorean Theorem.

AssignmentO Pg. 19 #17-21 odds, 25-33 odds