Answer:
[tex]\left(\boxed{\quad 14\quad }, \boxed{\quad -4\quad }\right)[/tex]
Step-by-step explanation:
To find the coordinates of point B, we'll use the midpoint formula.
The midpoint formula states that the midpoint [tex] C [/tex] between two points [tex] (x_1, y_1) [/tex] and [tex] (x_2, y_2) [/tex] is given by:
[tex] \Large\boxed{\boxed{C\left(\dfrac{{x_1 + x_2}}{2}, \dfrac{{y_1 + y_2}}{2}\right)}} [/tex]
Given that point [tex] A [/tex] is located at [tex] (2,6) [/tex] and the midpoint [tex] C [/tex] is [tex] (8,1) [/tex], we can find the coordinates of point [tex] B [/tex].
Let's denote the coordinates of point [tex] B [/tex] as [tex] (x, y) [/tex].
Using the midpoint formula, we have:
[tex] \dfrac{{2 + x}}{2} = 8 [/tex]
[tex] \dfrac{{6 + y}}{2} = 1 [/tex]
From the first equation:
[tex] 2 + x = 2 \times 8 [/tex]
[tex] x + 2 = 16 [/tex]
[tex] x = 16 - 2 [/tex]
[tex] x = 14 [/tex]
From the second equation:
[tex] 6 + y = 2 \times 1 [/tex]
[tex] y + 6 = 2 [/tex]
[tex] y = 2 - 6 [/tex]
[tex] y = -4 [/tex]
Therefore, the coordinates of point B are:
[tex] \Large\boxed{\boxed{(14, -4) }}[/tex]
