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.

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Presentation transcript:

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 segment from A to B

The Distance Formula The distance d between the points (x 1, y 1 ) and (x 2, y 2 ) is: how far away the two points are

Find the distance between the points (2, 8) and (-1, 6). Let (x 1,y 1 ) = (2, 8) and (x 2, y 2 ) = (-1, 6):

Find the distance between the points (-2, 5) and (3, -1). Let (x 1, y 1 ) = (-2, 5) and (x 2, y 2 ) = (3, -1):

The Midpoint Formula The midpoint m between the two points (x 1, y 1 ) and (x 2, y 2 ) is: the middle of the two ordered pairs

Find the midpoint of the segment whose endpoints are (6, -2) and (2, -9). Let (x 1, y 1 ) = (6, -2) and (x 2, y 2 ) = (2, -9):

Find the midpoint of the segment whose endpoints are (-8, -4) and (2, 5). Let (x 1, y 1 ) = (6, -2) and (x 2, y 2 ) = (2, -9):

Application Nike and Vada ran away from Mr. V on a walk the other day. They run equally fast in opposite directions, leaving Mr. V right in the middle. On a map of the Fox Valley area, Nike ends up at the ordered pair (-2, -13) and Vada ends up at (14, 39). Nike and Vada ran away from Mr. V on a walk the other day. They run equally fast in opposite directions, leaving Mr. V right in the middle. On a map of the Fox Valley area, Nike ends up at the ordered pair (-2, -13) and Vada ends up at (14, 39). –What is the ordered pair that corresponds to Mr. V’s location? –How far away are Nike and Vada away from each other after they run away? Assume that the ordered pairs on the map are spaced out by meters.

(-2, -13) (14, 39) (?, ?)

Application Nike and Vada ran away from Mr. V on a walk the other day. They run equally fast in opposite directions, leaving Mr. V right in the middle. On a map of the Fox Valley area, Nike ends up at the ordered pair (-2, -13) and Vada ends up at (14, 39). Nike and Vada ran away from Mr. V on a walk the other day. They run equally fast in opposite directions, leaving Mr. V right in the middle. On a map of the Fox Valley area, Nike ends up at the ordered pair (-2, -13) and Vada ends up at (14, 39). –What is the ordered pair that corresponds to Mr. V’s location? –How far away are Nike and Vada away from each other after they run away? Assume that the ordered pairs on the map are spaced out by meters. (6, 13) 54.4 meters

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