State whether the following statement is true or false. Justify your answer.
Point $P (-4, 2)$ lies on the line segment joining the points $A (-4, 6)$ and $B (-4, -6)$.

(TRUE) True.
Analytical Justification:
$1$. The points $A (-4, 6)$ and $B (-4, -6)$ have the same $x$-coordinate,which is $-4$. This means the line segment $AB$ is a vertical line represented by the equation $x = -4$.
$2$. The point $P (-4, 2)$ also has an $x$-coordinate of $-4$,so it lies on the line $x = -4$.
$3$. For $P$ to lie on the line segment $AB$,its $y$-coordinate must be between the $y$-coordinates of $A$ and $B$. The $y$-coordinates of $A$ and $B$ are $6$ and $-6$ respectively.
$4$. Since $-6 < 2 < 6$,the point $P$ lies between $A$ and $B$ on the line segment $AB$.