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D,E,F are the mid - points of the sides ...

D,E,F are the mid - points of the sides `overline(BC),overline(CA)andoverline(AB)` respectively of the triangle ABC , using coordinate geometry show that , `3(BC^(2)+CA^(2)+AB^(2))=4(AD^(2)+BE^(2)+CF^(2))`.

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CHHAYA PUBLICATION-REVISION OF PREVIOUS TWO DIMENSIONAL COORDINATE GEOMETRY -EXERCISE 1 ( Long Type Questions )
  1. The points P,Q,R are collinear , if the coordinates of P and Q be (3,4...

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  2. The coordinates of the points A,B,C D are respectively (6,3) , (-3,5) ...

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  3. The coordinates of the points A,B,C and D are (-2,3), (8,9), (0,4) and...

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  4. The coordinates of the points A and B are (3,4) and (5,-2) respective...

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  5. The area of a quadrilateral is 28 square unit. If the coordinates of i...

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  6. If x(1),x(2),x(3) as well as y(1),y(2),y(3) are in G.P. with the sa...

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  7. Shift the origin to a suitable point so that the equation 2x^(2)-4x+3y...

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  8. Find the point to which the origin should be shifted so that the equat...

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  9. Show that the distance between two points remains unaltered by the tra...

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  10. Reduce the equation x+y+5=0 andx-2y+2=0 to the form ax+by =0 by prope...

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  11. Choose a new origin (h,k) (retaining the directions of axes) so that t...

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  12. Find the distance between the point (1+sqrt2,1-sqrt2) and (0,0)

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  13. Show that the straight line joining the mid - points of two sides of a...

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  14. Show that the straight lines joining the mid - points of the opposite ...

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  15. Prove analytically that the area of a triangle is four times that of t...

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  16. Using analytical method prove that the mid - point of the hypotenuse o...

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  17. If two medians of a triangle are equal , prove analytically that the t...

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  18. Using coordinate geometry prove that an isosceles traigle has two equa...

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  19. D,E,F are the mid - points of the sides overline(BC),overline(CA)andov...

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  20. ABC is a right angled triangle right angled at B. If P and Q are the m...

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