anonymous
  • anonymous
Can someone help me review the distance formula and how to calculate a midpoint?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
ok, sure...do you have any points to work with?
anonymous
  • anonymous
Hold on and I'll get a few my teacher gave me to work with
anonymous
  • anonymous
sure

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anonymous
  • anonymous
W(3, -12) M(2, -1)
anonymous
  • anonymous
M is the midpoint
anonymous
  • anonymous
ok, good start. so draw it on a graph first
anonymous
  • anonymous
Ok one second
anonymous
  • anonymous
you need to find the other point, let's call it P...
anonymous
  • anonymous
Ok i have the graph drawn
anonymous
  • anonymous
nice, so what is the midpoint formula?
anonymous
  • anonymous
(X1+x2)/2 ; (Y1+y2)/ 2
anonymous
  • anonymous
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
anonymous
  • anonymous
we have that \[2 = (x1 + x2) / 2]\, and that x1 = the x-coordinate from W
anonymous
  • anonymous
x1 = 3, x2 = ? --> 2 = ( 3 + x2 )/2...solve for x2
anonymous
  • anonymous
what did you get?
anonymous
  • anonymous
this would be the x-coordinate for the point P we made up
anonymous
  • anonymous
I got -2 for X2
anonymous
  • anonymous
hey, you can refresh the page when it gets stuck ;)
anonymous
  • anonymous
ok.. I was freaking there for a sec
anonymous
  • anonymous
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
anonymous
  • anonymous
So this is how I got -2 for an answer 2=(3+X2)/2 -3 -3 (-1)=X2/2 x2 x2 -2= X2
anonymous
  • anonymous
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
anonymous
  • anonymous
Oh... okay. I didn't know to do that.
anonymous
  • anonymous
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
anonymous
  • anonymous
*can't get the 3...
anonymous
  • anonymous
you want to try the same process to find y?
anonymous
  • anonymous
Alright.. Thanks for telling me that, my math teacher thought it was okay not to tell us that. And if you want too.
anonymous
  • anonymous
yes, let's solve for the y-coordinate of P...we have P = ( x2, y2 ) --> P = ( 1, y2 )
anonymous
  • anonymous
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
anonymous
  • anonymous
Okay
anonymous
  • anonymous
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...
anonymous
  • anonymous
Is it possible to use the slope intercept to find Y? or would that just add confusion?
anonymous
  • anonymous
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!
anonymous
  • anonymous
I ended up getting -14
anonymous
  • anonymous
what are your steps? remember that you have to multiply by 2 here before dealing with -12
anonymous
  • anonymous
(-12 + Y2)/2=-1 *2 *2 (-12 + y2)= -2 +-12 +-12 Y2= -14
anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
right, so what are the coordinates of our point P?
anonymous
  • anonymous
Okay, so the -2 we divided by is still on the right side of the equal sign?
anonymous
  • anonymous
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
anonymous
  • anonymous
sorry, :(, I have to go, but I will be back in 15-20minutes
anonymous
  • anonymous
once you get the midpoint stuff down, you can work on the the distance formula, which is: \[d = \sqrt{ (x2 - x1)^2 + (y2 - y1)^2 }\]
anonymous
  • anonymous
so, brb
anonymous
  • anonymous
Okay I'll be here
anonymous
  • anonymous
all right, are you finished with midpoint stuff?

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