The line segment joining $A(-3, 5)$ and $B(2, 5)$ intersects............

Two vertices of a triangle are $A(2, 1)$ and $B(3, -2)$. The third vertex is $C(x, y)$,where $y = x + 3$. If the area of the triangle is $5$,find the coordinates of the third vertex.

Find the area of a triangle having the vertices $A(3, 2), B(11, 8)$ and $C(8, 12)$.

If $A(0, y_{1})$ and $B(0, y_{2})$ are the points on the $Y$-axis,then the distance between them $AB = \ldots$

If the point $A (2, -4)$ is equidistant from $P (3, 8)$ and $Q (-10, y)$,find the values of $y$. Also,find the distance $PQ$.

State whether the following statement is true or false. Justify your answer.
Point $P(5, -3)$ is one of the two points of trisection of the line segment joining the points $A(7, -2)$ and $B(1, -5)$.