Let the unknown endpoint be (x₂ , y₂) and the known (x₁ , y₁)
mid-point = [tex]( \frac{x_{1} + x_{2} }{2} , \frac{y_{1} + y_{2} }{2} ) [/tex] = (A , B)
plug in the known values
=> [tex]( \frac{-3 + x_{2} }{2} , \frac{5 + y_{2} }{2} ) [/tex]
separate the two parts of the equation for the formula and solve
for the value of the unknown y and x
=> A : [tex] \frac{-3 + x_{2} }{2} = 5
[/tex]
-3 + x₂ = (5)(2)
x₂ = 10 + 3
= 13
B: [tex] \frac{5 + y_{2} }{2} = 2
[/tex]
5 + y₂ = (2)(2)
5 + y₂ = 4
y₂ = 4 - 5
= - 1
∴ if midpoint is (A,B) then midpoint is (13 , -1)
