Verified Answer :

ceciliamachado2

so to find the other endpoint you need to see  how far the first endpoint is to the midpoint. In X's place we have a total distance of
5- (-3)= 8 place away from one another so 
5+8= 13

while in the y's case 
5-2=3 place away from one another so 
2-3= -1

so your order pair is 
(13,-1)

JoshEast

Let the unknown endpoint be (x₂ , y₂) and the known (x₁ , y₁)

mid-point  =  \(( \frac{x_{1} + x_{2} }{2} , \frac{y_{1} + y_{2} }{2} )\) = (A , B)
              plug in the known values
     
        =>    \(( \frac{-3 + x_{2} }{2} , \frac{5 + y_{2} }{2} )\)
       
       separate the two parts of the equation for the formula and solve
                         for the value of the unknown y and x 
   
         =>   A :  \(\frac{-3 + x_{2} }{2} = 5\)
                       -3  +  x₂  =  (5)(2)
                                x₂  =  10 + 3
                                      =  13
 
                B:  \(\frac{5 + y_{2} }{2} = 2\)
                        5  +  y₂   =  (2)(2)
                        5  +  y₂   =  4
                                y₂   = 4 - 5
                                      =  - 1

∴  if midpoint is (A,B)  then midpoint is  (13 , -1)


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