Given parameters:
Midpoint of AB = M(3, -1)
Coordinates of A = (5,1)
Unknown:
Coordinates of B = ?
Solution:
To find the mid point of any line, we use the expression below;
[tex]x_{m} = \frac{x_{1} + x_{2} }{2}[/tex] and [tex]y_{m} = \frac{y_{1} + y_{2} }{2}[/tex]
where [tex]x_{m}[/tex] and [tex]y_{m}[/tex] = coordinates of the mid points = 3 and -1
x₁ = 5 and y₁ = 1
x₂ = ? and y₂ = ?
Now let us input the variables and solve,
3 = [tex]\frac{5 + x_{2} }{2}[/tex] and -1 = [tex]\frac{1 + y_{2} }{2}[/tex]
5 + x₂ = 6 -2 = 1 + y₂
x₂ = 1 y₂ = -2 -1 = -3
The coordinates of B = 1, -3
