Coordinate Geom...

The points $$( - a , - b ) , ( 0,0 ) , ( a , b ) , \left( a ^ { 2 } , a b \right)$$ are

If $$P \left( \dfrac{a}{3},\dfrac{b}{2} \right)$$ is the mid-point of the line segment joining $$A(-4,3)$$ and $$B(-2,4)$$, then $$(a,b)$$ is 

The line segment joining the points $$(1, 2)$$ and $$(k, 1)$$ is divided by the line $$3x + 4y - 7 = 0$$ in the ratio $$4 : 9$$ then $$k$$ is 

If area of a triangle is $$35$$ square units with vertices $$\left( {2, - 6} \right),\,\,\left( {5,\,\,4} \right)$$ and $$({k},\,\,4)$$ then $${k}$$ is :

If the ratio in which the line segment joining the points (6,4) and (x,-7) divided internally by y-axis is 6: 1, then x equals

If $$(-6,-4)$$ and $$(3,5)$$ are the extremities of the diagonals of a parallelogram and $$(-2,1)$$ is its third vertex, then its fourth vertex is 

If $$P\left(\dfrac{a}{3},4\right)$$  is the mid point of the line segment joining the points $$(-6,5),(-2,3).$$ Then, find the value of $$a.$$

The mid-point of the line joining the points $$(2p +2, 3)$$ and $$(4, 2q + 1)$$ is $$(2p, 2q)$$, then

If the mid point of $$(6, 8)$$ and $$(8, 6)$$ is mid point of $$(10, 3)$$ and $$(x, y)$$, then $$x + y$$ is

The area of a triangle with vertices $$A(5,0),B(8,0)$$ and $$C(8,4)$$ in square units is