Question

A, B, and C, are points on a number line. The coordinate of A is -12, the coordinate of B is 2, and the coordinate of C is 9. Does AB+BC=AC? Is B the midpoint of AC? If not, what is the coordinate of the midpoint?

Answer 1

i think may be more usefully than drawn these points

Answer 2

AB = distance between -12 and 2
BC = distance between 2 and 9

AC = distance between -12 and 9...

Answer 3

first calculate these distances, check if they are equal. this answers your first question

B is only the midpoint of AC, if AB=BC

Answer 4

distance AC=18?

Answer 5

why just 18 ?

Answer 6

wait....

Answer 7

on the left of zero there are 12 units and on the right of zero there are 9 units aod adding these how many will get ?

Answer 8

AB=-10

Answer 9

can i do for finding BC: 9-2? or is it -2+9

Answer 10

either way?

Answer 11

am i right?

Answer 12

no

AB not equal -10 bc. a distance not can being negtiv - right ?

Answer 13

then 10?

Answer 14

so for you get the distance of AB just you need assuming the units between A and B and so between A and C

Answer 15

distance is absolute value
i.e. AB can be | B - A | or | A - B|

Answer 16

so then 10

Answer 17

no

Answer 18

then what is it?

Answer 19

between A and zero there are 12 units - yes ?
and from zero till B are 2 units so 12+2 = ?

Answer 20

ok. ?

Answer 21

example\[AB=|-12-2|=|2-(-12)|\]

Answer 22

@silvernight269 how are you doing? Should we start over?

Answer 23

yes

Answer 24

im soooooooooo confused rn.

Answer 25

\(\color{#0cbb34}{\text{Originally Posted by}}\) @kittybasil
Quote:
AB = distance between -12 and 2
BC = distance between 2 and 9

AC = distance between -12 and 9...


part 1
1. calculate AB and BC
2. calculate AC
3. Does "AB + BC" = "AC" ?

part 2
1. Are "AB" and "BC" equal?
\(\color{#0cbb34}{\text{End of Quote}}\)

Remember that distance is one point subtracted from the other, but in absolute value

Example: If you have two points, -5 and 3, and you want to find the distance between them, you can do either:\[D=|3-(-5)|\]or this:\[D=|(-5)-3|\] with "D" being the symbol representing distance.
Absolute value makes these equal as there is no negative sign in absolute value. The distances should be the same in both of those examples.

Answer 26

So let's calculate AB, which is from "-12" to "2"
You can either do \(|2-(-12)|\) or \(|-12-2|\) to find the distance.

Simplifying;
\(|2+12|=|14|=14\) and \(|-14|=14\). Both are the same.

Answer 27

Are you with me so far?

Answer 28

to find the midpoint wouldnt it be add the 2 numbers then divide by 2?

Answer 29

??? We are on the first part.

Did you solve this stuff already?

Answer 30

nope

Answer 31

Ok, so we can keep going then?
I assume we're working on "Does AB+BC=AC?"

Answer 32

yes

Answer 33

Okay.

Are you good so far? I can explain anything you are stuck on :)

Answer 34

If you need to go back and read through anything, take your time :D

Answer 35

ok thanks

Answer 36

ok i found the first 2 questions.
now the last one

Answer 37

Wait, what were your results O.o

Answer 38

first question is a yes, 2nd is a no.

Answer 39

Hmm
@dude can you check cause I'm not in a place I can write this out lol

Answer 40

btw, I have to do something, but the midpoint is "Distance of AC" divided by 2

Answer 41

ok so 21 /2?

Answer 42

Okay for the first q, its yes
B is not the midpoint of AC

Yes midpoints is 21/2

Answer 43

ok i got it