Find the coordinates of the other endpoint if the midpoint is M(8, 2) and the other endpoint is P(5, 6). (6.5, 4) (21, 10) (11, -2) Help? Please

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Find the coordinates of the other endpoint if the midpoint is M(8, 2) and the other endpoint is P(5, 6). (6.5, 4) (21, 10) (11, -2) Help? Please

Mathematics
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Alright, which formula do you think will help you solve this?
I want to say midpoint but that's not right
It is right. :)

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Okay. So you already know your midpoint. Do you realize that midpoint breaks into two separate parts in order to solve right? We solve for x, and then for y?
Okay, so how do you break it into two parts?
Well let's do the x value first shall we? Midpoint formula looks like this: [(x_1 + x_2)/2 , (y_1 + y_2)/2] ----IN TOTAL But let's look at it in parts. To solve for Xm m=midpoint \[\frac{ x1+x2 }{ 2 }\] That's x-value 1 and 2 btw. So I'll show you how to set up and how to find X-value we are looking for. Let's call the point we are looking for, x-value 1. and we know that the Xm is 8. Have you followed what I am saying so far?
Yes
Great! So let's plug values in that we know. \[\frac{ x1+5 }{ 2 }= 8\] --------I took the 5 from the x-value from point P and the 8 is the x-value from Midpoint.
Following?
Okay, but how did you get 8?
Remember, Midpoint formula is used to find the midpoint. We were given the x-value of 8 as your midpoint in the question. We are using Midpoint formula in order to find your other point.
\[\frac{ x1+x2 }{ 2 }=Xm\]
Oh right. Sorry I got confused
Refer to that if it helps you understand why I picked which points. :)
Alright so we can continue?
Yes please
Alright, now here's the part where I want to see if you can solve for the x-value by yourself. I set up the equation for you, now please solve for x1. I will check it for you. :) \[\frac{ x1+5 }{ 2 }=8\]
Don't you first multiply everything by 2 to get rid of the fraction?
Correct.
so is it x1+10=16? is that correct so far?
You don't multiply the 2 by the 5. When you multiple the 2 to get rid of the fraction then it cancels from the first side leaving you with only x1+5 and the other side being 16. Got it?
Oh. okay, yes got it
so x1=11
Good! Now can you set up the equation for y-value and try to solve that? It's the same steps in plugging and solving. Try it! :)
So the answer is 11, -2?
Perfect!
Don't forget parenthesis
Thank you :)
You are welcome. :D

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