Find the point on the $X$-axis which is equidistant from $(5, 4)$ and $(-2, 3)$.

If the vertices of $\Delta ABC$ are $A(-4, -1)$,$B(1, 2)$,and $C(4, -3)$,then the area of the triangle is:

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.

If one vertex of a triangle is $(1, 1)$ and the midpoints of the sides through this vertex are $(-1, 2)$ and $(3, 2)$,then find the centroid of the triangle.

In $\Delta ABC$,$A(1, 2)$,$B(3, 4)$,and $C$ lies on the $X$-axis. If the centroid $G$ of $\Delta ABC$ is on the $Y$-axis,then find the coordinates of $C$.

The distance between the points $A(a+b, b-a)$ and $B(a-b, a+b)$ is............