Question

what is the distance formula?

Answer 1

suppose you want to find the distance between two points (x1,y1) and (x2,y2)
the distance formula is
=sqrt((x1-x2)^2+(y1-y2)^2)

Answer 2

\[d = \sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\]

Answer 3

Which in essence is simply Pythagoras theorem, if you form an 'imaginary' triangle between the two points.

Answer 4

okay i have to find the distance between (5,5) and (10,2)

Answer 5

then take (5,5) as (x1,y1)
and (10,2) as (x2,y2) then put these values in require formula

Answer 6

is it 14?

Answer 7

how did you get that?

Answer 8

idkk.im not sure what the answer is

Answer 9

did you just guess at 14? the instructions provided by the two posters are pretty clear...

Answer 10

no i just didnt plug it in right.whats the answer then?

Answer 11

i can't directly give you the answer... but i can make you give me the answer....

Answer 12

k?

Answer 13

what's \(\large x_2-x_1= \) and \(\large y_2-y_1= \)

Answer 14

2 and -3?

Answer 15

no...
\(\large x_2-x_1= \) refers to subtracting the x coordinates... what are the x coordinates?

Answer 16

arent they 5 and 10?

Answer 17

yes... now subtract those two x values...

Answer 18

-5

Answer 19

good. now
\(\large (x_2-x_1)^2=(-5)^2=25 \), agreed?

Answer 20

yess

Answer 21

good... i want you to do the exact same thing with the y-coordinates....
find me \(\large (y_2-y_1)^2= \)

Answer 22

its 9 right?

Answer 23

correct... so in the distance formula:
\(\large d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{25+9} \)
can you simplify it from here?

Answer 24

is it 5.83?

Answer 25

if that's what your calculator gave you for \(\large \sqrt{34} \), then yes...

Answer 26

yupp it did

Answer 27

the exact way to write your answer is \(\large \sqrt{34} \)

Answer 28

wasn't that better than guessing? :)

Answer 29

it tells me to round my answer to the nearest tenth though

Answer 30

oh.. ok....:)

Answer 31

thank you so much:)

Answer 32

yw...:)

Answer 33

can you help me find the midpoint of (7,9) and (12,11)

Answer 34

it is equal to( x1+x2)/2,(y1+y2)/2.
here (x1,y1) is (7,9) and (x2,y2) is (12,11)

Answer 35

midpoint =(7+12)/2,(9+11)/2

Answer 36

9.5,10?

Answer 37

yes