Question

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

Answer 1

Alright, which formula do you think will help you solve this?

Answer 2

I want to say midpoint but that's not right

Answer 3

It is right. :)

Answer 4

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?

Answer 5

Okay, so how do you break it into two parts?

Answer 6

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?

Answer 7

Yes

Answer 8

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.

Answer 9

Following?

Answer 10

Okay, but how did you get 8?

Answer 11

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.

Answer 12

\[\frac{ x1+x2 }{ 2 }=Xm\]

Answer 13

Oh right. Sorry I got confused

Answer 14

Refer to that if it helps you understand why I picked which points. :)

Answer 15

Alright so we can continue?

Answer 16

Yes please

Answer 17

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. :)
\[\frac{ x1+5 }{ 2 }=8\]

Answer 18

Don't you first multiply everything by 2 to get rid of the fraction?

Answer 19

Correct.

Answer 20

so is it x1+10=16? is that correct so far?

Answer 21

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?

Answer 22

Oh. okay, yes got it

Answer 23

so x1=11

Answer 24

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! :)

Answer 25

So the answer is 11, -2?

Answer 26

Perfect!

Answer 27

Don't forget parenthesis

Answer 28

Thank you :)

Answer 29

You are welcome. :D