Question

Can someone help me review the distance formula and how to calculate a midpoint?

Answer 1

ok, sure...do you have any points to work with?

Answer 2

Hold on and I'll get a few my teacher gave me to work with

Answer 3

sure

Answer 4

W(3, -12) M(2, -1)

Answer 5

M is the midpoint

Answer 6

ok, good start. so draw it on a graph first

Answer 7

Ok one second

Answer 8

you need to find the other point, let's call it P...

Answer 9

Ok i have the graph drawn

Answer 10

nice, so what is the midpoint formula?

Answer 11

(X1+x2)/2 ; (Y1+y2)/ 2

Answer 12

ok cool, so you have W:(3, -12), and you have the midpoint...so M=(2,-1)...right so use the formulas. let's look at (x1+x2)/2

Answer 13

we have that \[2 = (x1 + x2) / 2]\, and that x1 = the x-coordinate from W

Answer 14

x1 = 3, x2 = ? --> 2 = ( 3 + x2 )/2...solve for x2

Answer 15

what did you get?

Answer 16

this would be the x-coordinate for the point P we made up

Answer 17

I got -2 for X2

Answer 18

hey, you can refresh the page when it gets stuck ;)

Answer 19

ok.. I was freaking there for a sec

Answer 20

the x-coordinate for W is 3, so you say x2 = -2, let's put that back in the Midpoint equation for X:

=> so we have 3 from W and now we have -2 from x2 , this is (3 + -2) = 1, then 1/2

but the goal is 2

Answer 21

So this is how I got -2 for an answer
2=(3+X2)/2
-3 -3
(-1)=X2/2
x2 x2
-2= X2

Answer 22

so you should multiply both sides by 2

1. 2 = ( 3 + x2 ) /2
2. Multiply both sides by 2 (to get ride of the 2 on the right side)
2*2 = ( 3 + x2 ) /2 *2
= 4 = (3 +x2)
3. now we have [ 4 = (3 + x2) ], solve for x2 get x2 = 1

Answer 23

Oh... okay. I didn't know to do that.

Answer 24

you skipped ahead and subtracted 3 from both sides, but 3 is in the parantheses. it's like we can get the 3 because the whole thing ( 3 + x2 ) is being divided by 2, so the equation actually is 3/2 + x2/2

Answer 25

*can't get the 3...

Answer 26

you want to try the same process to find y?

Answer 27

Alright.. Thanks for telling me that, my math teacher thought it was okay not to tell us that. And if you want too.

Answer 28

yes, let's solve for the y-coordinate of P...we have P = ( x2, y2 ) --> P = ( 1, y2 )

Answer 29

so you can look at your graph, and find 1 on the x-axis...now you're half way there to finding where P actually is

Answer 30

Okay

Answer 31

ok, so you're stuck at x=1, now you can only move up or down, changing y, so you have M on the graph and W on the graph, so you can make a guess at where P is just by checking out the graph...

Answer 32

Is it possible to use the slope intercept to find Y? or would that just add confusion?

Answer 33

you could, but you have a simple midpoint equation to find y... (y1 + y2) /2 = -1, with y1=-12, so ( -12 + y2 ) /2 = -1...solve it!

Answer 34

I ended up getting -14

Answer 35

what are your steps? remember that you have to multiply by 2 here before dealing with -12

Answer 36

(-12 + Y2)/2=-1
*2 *2
(-12 + y2)= -2
+-12 +-12
Y2= -14

Answer 37

ah, if you have -12 to both sides, you actually have (-24 + y2) = -14...so you should add 12 to both sides, to get y2 = -2 + 12 = 10

Answer 38

the goal was to get rid of -12 on the left side, but you can't just get rid of it, you have to keep the relationship that you already have....so if you get rid of -12 on the left side by adding 12 (thus getting 0), you have to do the same thing to the right side or else you've changed the relationship...it's all about find ways to reduce the problem

Answer 39

right, so what are the coordinates of our point P?

Answer 40

Okay, so the -2 we divided by is still on the right side of the equal sign?

Answer 41

right, you multiplied each side by 2 to get rid of the /2 on (y1 + y2), that would make the right side (-1) * (2) = -2

Answer 42

sorry, :(, I have to go, but I will be back in 15-20minutes

Answer 43

once you get the midpoint stuff down, you can work on the the distance formula, which is: \[d = \sqrt{ (x2 - x1)^2 + (y2 - y1)^2 }\]

Answer 44

so, brb

Answer 45

Okay I'll be here

Answer 46

all right, are you finished with midpoint stuff?