State whether the following statement is true or false. Justify your answer.
Point $P(0, 2)$ is the point of intersection of the $y$-axis and the perpendicular bisector of the line segment joining the points $A(-1, 1)$ and $B(3, 3)$.

(B) False.
We know that any point lying on the perpendicular bisector of a line segment is equidistant from the endpoints of that segment.
Let us calculate the distance of point $P(0, 2)$ from points $A(-1, 1)$ and $B(3, 3)$ using the distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
$PA = \sqrt{(0 - (-1))^2 + (2 - 1)^2} = \sqrt{(1)^2 + (1)^2} = \sqrt{1 + 1} = \sqrt{2}$.
$PB = \sqrt{(0 - 3)^2 + (2 - 3)^2} = \sqrt{(-3)^2 + (-1)^2} = \sqrt{9 + 1} = \sqrt{10}$.
Since $PA \neq PB$,the point $P(0, 2)$ is not equidistant from $A$ and $B$.
Therefore,the point $P(0, 2)$ does not lie on the perpendicular bisector of the line segment $AB$.