Take note Key Concept: Distance Formula

The distance between two points A ( x 1 , y 1 ) eh . open , x sub 1 , comma , y sub 1 , close  and B ( x 2 , y 2 ) b . open , x sub 2 , comma , y sub 2 , close  is

d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 d equals . square root of open . x sub 2 , minus , x sub 1 . close squared . plus . open . y sub 2 , minus , y sub 1 . close squared end root

Problem 3 Finding Distance

GRIDDED RESPONSE

What is the distance between U ( − 7 , 5 ) u open negative 7 comma 5 close  and V ( 4 , − 3 ) ? v open 4 comma negative 3 close question mark  Round to the nearest tenth.

Let U ( − 7 , 5 ) u open negative 7 comma 5 close  be ( x 1 , y 1 ) open , x sub 1 , comma , y sub 1 , close  and V ( 4 , − 3 ) v open 4 comma negative 3 close  be ( x 2 , y 2 ) . open , x sub 2 , comma , y sub 2 , close .

d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Use the Distance Formula .   = ( 4 − ( − 7 ) ) 2 + ( − 3 − 5 ) 2 Substitute .   = ( 11 ) 2 + ( − 8 ) 2 Simplify within the parentheses .   = 121 + 64 Simplify .   = 185     185 13.60147051 Use a calculator. table with 6 rows and 3 columns , row1 column 1 , d , column 2 equals . square root of open . x sub 2 , minus , x sub 1 . close squared . plus . open . y sub 2 , minus , y sub 1 . close squared end root , column 3 cap usethecap distancecap formula . . , row2 column 1 , , column 2 equals . square root of open . 4 minus . open , negative 7 , close . close squared . plus . open , negative 3 minus 5 , close squared end root , column 3 cap substitute . . , row3 column 1 , , column 2 equals . square root of open 11 close squared . plus . open , negative 8 , close squared end root , column 3 cap simplifywithintheparentheses . . , row4 column 1 , , column 2 equals . square root of 121 plus 64 end root , column 3 cap simplify , . , row5 column 1 , , column 2 equals , square root of 185 , column 3 , row6 column 1 , , column 2 185

To the nearest tenth, U V = 13 . 6 . u v equals 13 . 6 .

✓ Got It?

3. 1. S R ¯ s r bar  has endpoints S ( − 2 , 14 ) s open negative 2 comma 14 close  and R ( 3 , − 1 ) . r open 3 comma negative 1 close .  What is SR to the nearest tenth?
   2. Reasoning In Problem 3, suppose you let V ( 4 , − 3 ) v open 4 comma negative 3 close  be ( x 1 , y 1 ) open , x sub 1 , comma , y sub 1 , close  and U ( − 7 , 5 ) u open negative 7 comma 5 close  be ( x 2 , y 2 ) . open , x sub 2 , comma , y sub 2 , close .  Do you get the same result? Why?