Consider the points $A$ and $B$ with respective coordinates in an orthonormal coordinate system: $$A ( 2 ; 0 ) \text { and } \mathrm { B } ( 0 ; - 4 ) \text {. }$$ VII-A- An equation of the line $( A B )$ is $2 x - y - 4 = 0$. VII-B- An equation of the perpendicular bisector of segment $[ A B ]$ is $x + 2 y + 3 = 0$. VII-C- An equation of the circle with diameter $[ A B ]$ is $x ^ { 2 } + y ^ { 2 } - 2 x - 4 y = 0$. VII-D- The point with coordinates $( - 1 ; - 1 )$ belongs to the circle with diameter $[ A B ]$. VII-E- The line with equation $2 x - y + 1 = 0$ is tangent to the circle with diameter $[ A B ]$. For each statement, indicate whether it is TRUE or FALSE.
\section*{Exercise VII}
Consider the points $A$ and $B$ with respective coordinates in an orthonormal coordinate system:
$$A ( 2 ; 0 ) \text { and } \mathrm { B } ( 0 ; - 4 ) \text {. }$$
VII-A- An equation of the line $( A B )$ is $2 x - y - 4 = 0$.\\
VII-B- An equation of the perpendicular bisector of segment $[ A B ]$ is $x + 2 y + 3 = 0$.\\
VII-C- An equation of the circle with diameter $[ A B ]$ is $x ^ { 2 } + y ^ { 2 } - 2 x - 4 y = 0$.\\
VII-D- The point with coordinates $( - 1 ; - 1 )$ belongs to the circle with diameter $[ A B ]$.\\
VII-E- The line with equation $2 x - y + 1 = 0$ is tangent to the circle with diameter $[ A B ]$.
For each statement, indicate whether it is TRUE or FALSE.