Q8 of 184 Page 10

The vertices of ΔABC are A(3, 0), B(0, 6) and (6, 9). A straight line DE divides AB and AC in the ratio 1:2 at D and E respectively, prove that

Given, ABC is a triangle with vertices A(3, 0), B(0, 6) and C (6, 9)


To find:


We know that


Area of triangle


Now Area of triangle DEF




square units


Now, According to the question,


DE internally divides AB in the ratio 1:2 hence


Coordinates of D




= (2, 2)


E internally divides AC in the ratio 1:2 hence


Coordinates of D




= (4, 3)


Now Area of triangle ADE




square units


Therefore, Area of ∆ABC sq. units


Hence, Area of ABC = 9. Area of ADE


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