Answer:
B=(-5, 4)
The coordinates of BB are (-5, 4)(-5,4)
Step-by-step explanation:
To solve, we will follow the steps below;
mid point = m(-2,1)
coordinates A is (1,-2)
To find the coordinates B
We will use the formula
([tex]x_{m}[/tex],[tex]y_{m}[/tex]) = ([tex]x_{1}[/tex] + [tex]x_{2}[/tex] /2 , [tex]y_{1}[/tex] +[tex]y_{2}[/tex]/2)
from the question
([tex]x_{m}[/tex],[tex]y_{m}[/tex]) = (-2,1)
this implies
[tex]x_{m}[/tex] = -2 [tex]y_{m}[/tex] = 1
Also
A([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) B( [tex]x_{2}[/tex] ,[tex]y_{2}[/tex])
A(1, -2) B( [tex]x_{2}[/tex] ,[tex]y_{2}[/tex])
[tex]x_{1}[/tex]= 1 [tex]y_{1}[/tex] =-2
we are to look for [tex]x_{2}[/tex] and [tex]y_{2}[/tex]
[tex]x_{m}[/tex] = [tex]x_{1}[/tex] + [tex]x_{2}[/tex] /2
-2 = 1 + [tex]x_{2}[/tex] /2
multiply both-side by 2
-4 = 1+ [tex]x_{2}[/tex]
subtract 1 from both-side of the equation
-4-1 =[tex]x_{2}[/tex]
-5 = [tex]x_{2}[/tex]
[tex]x_{2}[/tex] = -5
Similarly,
[tex]y_{m}[/tex] = [tex]y_{1}[/tex] +[tex]y_{2}[/tex]/2
1 = -2+[tex]y_{2}[/tex]/2
multiply both-side of the equation by 2
2 = -2 +[tex]y_{2}[/tex]
add 2 to both-side of the equation
2+2 = -2+ 2 +[tex]y_{2}[/tex]
4=[tex]y_{2}[/tex]
[tex]y_{2}[/tex] = 4
The coordinates of BB are (-5, 4)(-5,4)
