Answer :
Answer: B(8, -8 )
Step-by-step explanation: The formula for calculating mid - point between two points is given as :
M = ( [tex]\frac{x_{1}+x_{2}}{2}[/tex] , [tex]\frac{y_{1}+y_{2}}{2}[/tex] )
The mid point has been given from the question .
[tex]x_{1}[/tex] = -2
[tex]x_{2}[/tex] = ?
[tex]y_{1}[/tex] = 4
[tex]y_{2}[/tex] = ?
substituting into the formula , we have
(3 , - 2 ) = ([tex]\frac{-2+x_{2}}{2}[/tex] , [tex]\frac{4+y_{2}}{2}[/tex] )
Equating x -component to x and y component to y , we have
3 = [tex]\frac{-2+x_{2}}{2}[/tex]
cross multiplying , we have
6 = -2 + [tex]x_{2}[/tex]
Therefore:
[tex]x_{2}[/tex] = 8
Also , equating y component to y , we have
-2 = [tex]\frac{4+y_{2}}{2}[/tex]
-4 = 4 + [tex]y_{2}[/tex]
[tex]y_{2}[/tex] = -8
Therefore :
[tex]x_{2}[/tex] = 8
[tex]y_{2}[/tex] = -8
check
-2 + 8 / 2 = 3 and
-8 + 4 / 2 = -2