10.1 – The Distance and Midpoint Formulas. Geometry Review What is the difference between the symbols AB and AB? segment from A to B The length of the.

10.1 – The Distance and 10.1 – The Distance and Midpoint FormulasMidpoint Formulas

Geometry ReviewGeometry Review

What is the difference between What is the difference between the symbols AB and AB?the symbols AB and AB?

segment segment from A to Bfrom A to B

The The lengthlength of of the segment the segment from A to Bfrom A to B

The Distance FormulaThe Distance Formula

The The distancedistance dd between the between the points (points (xx11, , yy11) and () and (xx22, , yy22) is:) is:

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

how far away the two points arehow far away the two points are

Find the distance between the Find the distance between the points (2, 8) and (-1, 6).points (2, 8) and (-1, 6).

Let (xLet (x11,y,y11) = (2, 8) and (x) = (2, 8) and (x22, y, y22) = (-1, 6):) = (-1, 6):

2 2( 1 2) (6 8)d

9 4d

13 3.61d

Find the distance between the Find the distance between the points (-2, 5) and (3, -1).points (-2, 5) and (3, -1).

Let (Let (xx11, , yy11) = (-2, 5) and () = (-2, 5) and (xx22, , yy22) = (3, -1):) = (3, -1):

2 2(3 ( 2)) ( 1 5)d

25 36d

61 7.81d

The Midpoint FormulaThe Midpoint Formula

The The midpointmidpoint mm between the between the two points (two points (xx11, , yy11) and () and (xx22, , yy22) is:) is:

1 2 1 2( , )2 2

x x y ym

the middle of the two ordered pairsthe middle of the two ordered pairs

Find the midpoint of the Find the midpoint of the segment whose endpoints are segment whose endpoints are

(6, -2) and (2, -9).(6, -2) and (2, -9).Let (Let (xx11, , yy11) = (6, -2) and () = (6, -2) and (xx22, , yy22) = (2, -9):) = (2, -9):

6 2 2 9,

2 2

114,

2

Find the midpoint of the Find the midpoint of the segment whose endpoints are segment whose endpoints are

(-8, -4) and (2, 5).(-8, -4) and (2, 5).Let (Let (xx11, , yy11) = (6, -2) and () = (6, -2) and (xx22, , yy22) = (2, -9):) = (2, -9):

8 2 4 5,

2 2

13,

2

ApplicationApplication Nike and Vada ran away from Mr. V on a walk the Nike and Vada ran away from Mr. V on a walk the other day. They run equally fast in opposite other day. They run equally fast in opposite directions, leaving Mr. V right in the middle. On a directions, leaving Mr. V right in the middle. On a map of the Fox Valley area, Nike ends up at the map of the Fox Valley area, Nike ends up at the ordered pair (-2, -13) and Vada ends up at (14, 39).ordered pair (-2, -13) and Vada ends up at (14, 39).

– What is the ordered pair that corresponds to Mr. V’s What is the ordered pair that corresponds to Mr. V’s location?location?

– How far away are Nike and Vada away from each How far away are Nike and Vada away from each other after they run away? Assume that the ordered other after they run away? Assume that the ordered pairs on the map are spaced out by meters.pairs on the map are spaced out by meters.

(-2, -13)

(14, 39)

(?, ?)

ApplicationApplication Nike and Vada ran away from Mr. V on a walk the Nike and Vada ran away from Mr. V on a walk the other day. They run equally fast in opposite other day. They run equally fast in opposite directions, leaving Mr. V right in the middle. On a directions, leaving Mr. V right in the middle. On a map of the Fox Valley area, Nike ends up at the map of the Fox Valley area, Nike ends up at the ordered pair (-2, -13) and Vada ends up at (14, 39).ordered pair (-2, -13) and Vada ends up at (14, 39).

– What is the ordered pair that corresponds to Mr. V’s What is the ordered pair that corresponds to Mr. V’s location?location?

– How far away are Nike and Vada away from each How far away are Nike and Vada away from each other after they run away? Assume that the ordered other after they run away? Assume that the ordered pairs on the map are spaced out by meters.pairs on the map are spaced out by meters.

(6, 13)(6, 13)

54.4 meters54.4 meters

Homework:Homework:pgs. 592-593 #18-26 even (distance pgs. 592-593 #18-26 even (distance and midpoint for each)and midpoint for each)