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The vertices of A B C are A(4,\ 6),\...

The vertices of ` A B C` are `A(4,\ 6),\ \ B(1,\ 5)` and `C(7,\ 2)` . A line is drawn to intersect sides `A B` and `A C` at `D` and `E` respectively such that `(A D)/(A B)=(A E)/(A C)=1/4` . Calculate the area of ` A D E` and compare it with the area of ` A B C` .

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RD SHARMA-COORDINATE GEOMETRY-All Questions
  1. Find the area of the triangle formed by joining the mid-points of the ...

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  2. If P(1,\ 2),\ \ Q(1,\ 0) and R(0,\ 1) are the mid-points of the sid...

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  3. The vertices of A B C are A(4,\ 6),\ \ B(1,\ 5) and C(7,\ 2) . A l...

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  4. Find the area of the quadrilateral A B C D whose vertices are re...

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  5. Prove that the points (2,\ -2),\ (-3,\ 8) and (-1,\ 4) are colli...

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  6. For what value of x will the points (x ,\ -1),\ (2,\ 1) and (4,\...

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  7. Find the condition that the point (x ,\ y) may lie on the line j...

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  8. If the points (p ,\ q),\ (m ,\ n) and (p-m ,\ q-n) are collinear...

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  9. Find k so that the point P(-4,\ 6) lies on the line segment join...

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  10. If the coordinates of two points A and B are (3,\ 4) and (5,\ -2) re...

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  11. The coordinates of A ,\ B ,\ C are (6,\ 3),\ (-3,\ 5) and (4,\ -2) ...

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  12. If the points A(1,\ -2),\ \ B(2,\ 3),\ \ C(-3,\ 2) and D(-4,\ -3) a...

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  13. If the points P(-3,\ 9),\ \ Q(a ,\ b) and R(4,\ -5) are collinea...

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  14. Find the area of the triangle whose vertices are (6,\ 3),\ (-3,\ 5)...

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  15. Find the area of the quadrilateral whose vertices are (-3,\ 2),\ (5...

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  16. Find the area of the quadrilateral whose vertices taken in order are ...

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  17. Find the area of the quadrilateral whose vertices are (-4,\ -2),\ (...

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  18. The four vertices of a quadrilateral are (1,\ 2),\ (-5,\ 6),\ (7,\ ...

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  19. The vertices of A B C are (-2,\ 1),\ (5,\ 4) and (2,\ -3) respecti...

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  20. Show that the following sets of points are collinear. (2,\ 5),\ (4,...

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