The vertices of a `DeltaABC` are `A(3, 0), B (0, 6) and C (6, 9)`. A straight line DE divides AB and AC in the ration 1:2 at D and E respectively, prove that `(DeltaABC)/(DeltaADE) = 9`

The vertices of a triangle ABC are A(3,0), B(0,6) and C(6,9) . A line DE divides both AB and AC in the ratio 1 : 2 meeting AB in D and AC in E . Prove that DeltaABC=9DeltaADE .

The vertices of a DeltaABC are A(2, 3, 5), B(-1, 3, 2) and C (3,5,-2). The area of DeltaABC is

The vertices of a DeltaABC are A(4,6), B(1,5) and C(7,2). A line is drawn to intersect sides AB and AC at D and E respectively, such that (AD)/(AB)=(AE)/(AC)=1/4 Calculate the area of the DeltaA DE and compare it with the area of DeltaABC

The vertices of DeltaABC are A(-3,2) , B(0,3) and C(1,0) . Find the equation of the median through B .

The vertices of a DeltaABCare A(4,6),B(1,5)andC(7,2). A line is drawn to intersect side AB and AC at D and E respectively, such that (AD)/(AB)=(AE)/(AC)=1/4. Calculate the area of DeltaADE and compare it with the area of DeltaABC.

A line cuts two sides AB and AC of DeltaABC at points P and Q respectively. Prove (A(DeltaAPQ))/(A(DeltaABC))=(APxxAQ)/(ABxxAC) .

The co-ordinates of the vertices of a DeltaABC are A(1, 0) , B(3, 6) and C(3, 2) . Find the length of its medians.

If A, B, C are the points (-1, 5), (3, 1), (5, 7) respectively and D, E, F are the middle points of BC, CA and AB respectively, prove that : DeltaABC=4 DeltaDEF .

In DeltaABC, AB = AC and the bisectors of angleB and angleC meet AC and AB at point D and E respectively. Prove that BD = CE .

In the given figure, the sides AB and AC of DeltaABC have been extended to D and E respectively. If xgty , show that ABgtAC .