Answer:
[tex](2,\, 6)[/tex].
Step-by-step explanation:
Let [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex] denote the two endpoints.
The formula for the midpoint of these two points would be:
[tex]\displaystyle \left(\frac{x_{0} + x_{1}}{2},\, \frac{y_{0} + y_{1}}{2}\right)[/tex].
(Similar to taking the average of each coordinate.)
In this question, it is given that [tex]x_{0} = 10[/tex] whereas [tex]y_{0} = 12[/tex]. Substitute these two values into the expression for the coordinate of the midpoint:
- [tex]x[/tex]-coordinate of the midpoint: [tex]\displaystyle \frac{10 + x_{1}}{2} = 6[/tex].
- [tex]y[/tex]-coordinate of the midpoint: [tex]\displaystyle \frac{12 + y_{1}}{2} = 9[/tex].
Solve these two equations for [tex]x_{1}[/tex] and [tex]y_{1}[/tex]: [tex]x_{1} = 2[/tex] whereas [tex]y_{1} = 6[/tex].
Hence, the coordinate of the other point would be [tex](2,\, 6)[/tex].
