Coordinate Geom...

The point P divides the line segment joining the points $$\displaystyle A\left ( 2,1 \right )$$ and $$\displaystyle B\left ( 5,-8\right )$$ such that $$ \dfrac{AP}{AB}=\dfrac{1}{3}$$ If P lies on the line $$\displaystyle 2x+y+k=0$$
then the value of k is-

The midpoints of sides of a triangle are ($$3,4), (4,1)$$ and $$(2,0)$$. Which of the following is not the value of the coordinates of it's vertices?

The area of triangle formed by $$(0, 0), (0, a)$$ and $$(b, 0)$$ is .......... .

The end points of a diagonal of a parallelogram are $$(1, 3)$$ and $$(5, 7)$$, then the mid-point of the other diagonal is ..........

The midpoints of the sides of triangle $$ABC$$ are $$ (-1,-2), (6,1)$$ and $$(3,5) $$. The area of $$\displaystyle \triangle ABC$$ is ____ square units.

Area of triangle whose vertices are $$(0, 0), (2, 3), (5, 8)$$ is ____ square units.

The area of a triangle with the vertices $$(1, 2), (3, 4)$$ and $$(5, 6)$$, is ____ square units.

The coordinates of the points $$P$$ which divides $$(1, 0)$$ and $$(0, 0)$$ in $$1 : 2$$ ratio are .......... .

Find the area of $$\Delta ABC$$, in which $$A = (2, 1), B = (3, 4)$$ and $$C = (-3, -2).$$

If coordinates of P,Q, and R are (3,6),(-1,3) and (2,-1) respectively. Then area of $$\displaystyle \triangle PQR$$ is ____ square units.