First we need to know the coordinates of the movie theater, we can do this applying the midpoint formula:
[tex]\begin{gathered} P(BA,SR)=(\frac{10-6}{2},\frac{12-4}{2})\text{ = (}\frac{4}{2},\frac{8}{2}) \\ \Rightarrow P(BA,SR)=(2,4) \end{gathered}[/tex]We have that the movie theater is located at (2,4). Now we use this coordinates to find the location of Clara's house using again the midpoint formula:
[tex]\begin{gathered} P(MT,SR)=(\frac{-6+2}{2},\frac{4-4}{2})=(-\frac{4}{2},0) \\ \Rightarrow P(MT,SR)=(-2,0) \end{gathered}[/tex]Therefore, Clara's house is located at (-2,0)
