Coordinate Geom...

$$A(3,4)$$ and $$B(5,-2)$$ are two given points. If $$AP=PB$$ and area of $$\triangle {PAB}=10$$, then $$P$$ is -

If the area of triangle formed by the points $$(2a,b),(a+b,2b+a)$$ and $$(2b,2a)$$ be $$\lambda$$ then the area of the triangle whose vertices are $$(a+b,a-b), (3b-a,b+3a)$$ and $$(3a-b,3b-a)$$ will be

In a triangle $$ABC,A=(3,2),B=(1,4)$$ and the midpoint of $$AC$$ is $$(2,5)$$, then the mid point of $$BC$$ is

If $$A ( - 2, 5), B (3, 1)$$ and $$P,Q$$ are the points of intersection of $$AB$$ then mid-point of $$PQ$$ is

The area of the triangle vertices $$(1,0),(7,0)$$ and $$(4,4)$$ is ___ square units.

If $$A = ( 3 , - 4 )$$ and the midpoints of $$A B , A C$$ are $$( 2 , - 1 ) , ( 4 , - 5 )$$ respectively then the mid.point of $$B C$$ is 

The co -ordinates of the midpoint of a line segment joining $$ P(5,7) $$ and $$ Q (-3,3) $$ are........

The area of the quadrilateral formed by the points $$(1,1),(7,-3),(12,2)$$ and $$(7,21)$$ is 

The point which divides the line segment joining $$(-2, 4), (2, 7)$$ in the ratio $$2:1$$ internally is:

In the given figure (not drawn to scale), the coordinates of P, Q and R are (3, 0) (0, 5) and (0, -5) respectively. Find the area of $$\Delta PQR$$.