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The vertices of a triangle ABC are A(3,0...

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`.

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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

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MODERN PUBLICATION-STRAIGHT LINES -Revision exercise
  1. Show that the triangle, the coordinates of whose verticles are given b...

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  2. If a!=b!=c , prove that the points (a , a^2),(b , b^2),(c , c^2) can n...

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  3. The vertices of a triangle ABC are A(3,0), B(0,6) and C(6,9) . A line ...

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  4. A and A' be the points (5,0) and (-5,0) respectively. Find the equatio...

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  5. A B is a variable line sliding between the coordinate axes in such ...

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  6. Find the equation of the straight lines joining the points (acostheta(...

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  7. The extremities of the base of an isosceles triangle have coordinates ...

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  8. A line is such that its segment between the lines 5x -y+4=0 and 3x +4y...

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  9. Find the distance of the line 4x y = 0from the point P(4, 1) measure...

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  10. Show that the plane a x+b y+c z+d=0 divides the line joining the point...

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  11. Prove that (-1,4) is the orthocentre of the triangle formed by the lin...

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  12. The equation of the perpendicular bisector of the side AB of a triangl...

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  13. The opposite angular points of a square are (3,4) a) and (1,-1). Then ...

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  14. Using the concept of slope, prove that medians of an equilateral tr...

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  15. Show that the perpendicular drawn from the point (4,1) on the line seg...

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  16. A rectangle has two opposite vertices at the points (1,2)a n d(5,5)dot...

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  17. Find the coordinates of the incentre and centroid of the triangle whos...

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  18. The vertices of a triangle are A(x1, x1tantheta1),B(x2, x2tantheta2)a ...

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  19. The points (1, 3) and (5, 1) are two opposite vert of a rectangle. Th...

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  20. One side of a rectangle lies along the line 4x+7y+5=0. Two of its vert...

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