# Geometry

The midpoint of uv is (5 -11). the coordinates of one endpoint are u(3 5) find the coordinates of endpoint v. I really need help asap! i have to put this in today..

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1. let the other endpoint be (x,y)

I will find the x, then you find the y using the same method.

for the x:
(x+3)/2 = 5
x+3 = 10
x = 7

for the y:
......

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2. I don't know... i don't get it..

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3. the midpoint is just the average of the two endpoints.

Play around with a few numbers, and you will see that this is true.

Think of it this way.

You start at a, and b is halfway to c.

That is, (b-a) = (c-b)

The midpoint b can then be found:

b-a = c-b
2b = a+c
b = (a+c)/2

That's Reiny's method. Use that equation to find c.

Or, if you want to find c, then you can use

b-a = c-b
c = 2b-a
c = 2*5 - 3 = 7

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4. haha i know lol

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6. yes but how?

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7. (5,-11)=(3+x/2),(5+y/2)
5=3+x/2
Multiply each side by 2 and simplify.
-11=5+x/2
Multiply each side by 2 and simplify.

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8. logan paul

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9. there are two ways to solve.
the x value on point u is two away from the x value on the midpoint. two away from 5 is 7 so point v's x value is 7. the y value on u is 6 away from the y value on the midpoint. 6 away from 11 is 17 so v's y value is 17. v = (7 , 17)
the midpoint = (x1 + x2 / 2) + (y1 + y2 / 2)
(3 + x / 2) = 5
2 * (3 + x / 2) = 5 * 2 (this cancels put the /2 in the beginning of the problem)
(3 + x) = 10
-3 -3
x = 7
(5 + y / 2) = 11
multiply both sides by 2 again
(5 + y) = 22
subtract both sides by 5
y = 17

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