If three vertices of a parallelogram $ABCD$ are $A(1, 2)$,$B(2, 1)$,and $C(3, -4)$,then the coordinates of $D$ are.............

In what ratio does the $x$-axis divide the line segment joining the points $(-4, -6)$ and $(-1, 7)$? Find the coordinates of the point of division.

Let $A(4, 2), B(6, 5)$ and $C(1, 4)$ be the vertices of $\Delta ABC$. Find the coordinates of the centroid of the triangle.

When point $A(x_{1}, y_{1})$ and point $B(x_{2}, y_{2})$ are joined to form $\overline{AB}$ and a point divides $\overline{AB}$ in the ratio $\lambda : 1$,the coordinates of the point are:

Find the ratio in which the point $P \left(\frac{3}{4}, \frac{5}{12}\right)$ divides the line segment joining the points $A \left(\frac{1}{2}, \frac{3}{2}\right)$ and $B(2, -5)$. (in $: 5$)

$A (1, -2)$ and $B (-7, 1)$ are the given points. Find $P$ on the line segment $AB$ such that $P$ lies on the extension of $AB$ (as indicated by $P-A-B$ order,though the condition $3AP = 5AB$ implies $P$ is outside the segment $AB$) and $3AP = 5AB$.