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A(4,\ 2),\ B(6,5) and C(1,\ 4) are the ...

`A(4,\ 2),\ B(6,5)` and `C(1,\ 4)` are the vertices of ` A B C` . Find the coordinates of the points `Q` and `R` on medians `B E` and `C F` respectively such that `B Q : Q E=2:1` and `C R : R F=2:1` . What do you observe?

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To find the coordinates of points Q and R on the medians BE and CF of triangle ABC, we will follow these steps: ### Step 1: Identify the vertices of the triangle The vertices of triangle ABC are given as: - \( A(4, 2) \) - \( B(6, 5) \) - \( C(1, 4) \) ...
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RD SHARMA ENGLISH-COORDINATE GEOMETRY-All Questions
  1. A(4,\ 2),\ B(6,5) and C(1,\ 4) are the vertices of triangle A B C . ...

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  2. A(4,\ 2),\ B(6,5) and C(1,\ 4) are the vertices of A B C . Find th...

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  3. A(4,\ 2),\ B(6,5) and C(1,\ 4) are the vertices of A B C . Find th...

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  4. A B C D is a rectangle formed by joining the points A(-1,\ -1),\ \ ...

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  5. Show that A(-3,\ 2),\ \ B(-5,\ -5),\ \ C(2,\ -3) and D(4,\ 4) are the ...

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  6. Find the ratio in which the y-axis divides the line segment joining...

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  7. If the points A(6,\ 1),\ \ B(8,\ 2),\ \ C(9,\ 4) and D(k ,\ p) are ...

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  8. In what ratio does the point (-4,\ 6) divide the line segment jo...

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  9. Find the coordinates of a point A , here A B is a diameter of th...

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  10. Find the ratio in which the point P(-1,\ y) lying on the line se...

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  11. Points P ,\ Q ,\ R and S divide the line segment joining the points...

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  12. Find the ratio in which the point P(x ,\ 2) divides the line seg...

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  13. Find the ratio in which the line segment joining the points A(3,\ -...

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  14. Find the ratio in which the point P((3)/(4), (5)/(12)) divides the lin...

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  15. Find the coordinates of the centroid of a triangle whose vertices a...

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  16. Find the centroid of the triangle whose vertices are: (i)(1,\ 4),\ (...

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  17. Two vertices of a triangle are (1,\ 2),\ (3,\ 5) and its centroi...

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  18. If (-2,\ 3),\ (4,\ -3) and (4,\ 5) are the mid-points of the sides ...

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  19. In Fig. 14.40, a right triangle B O A is given. C is the mid-poi...

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  20. Find the third vertex of a triangle, if two of its vertices are at ...

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