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Prove that the four points (4,3),(6,4),(...

Prove that the four points (4,3),(6,4),(5,6) and (3,5) are the vertices of a square.

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Prove that the points A (-2,-1) , B (5,4) C (6,7) and D (-1,2) are the vertices of a parallelogram.

Calculating the angle of the triangle, prove that the points A(3, 4, -1) , B(1, 5, 1) and C(1, 2, -2) are the vertices of an isosceles triangle.

Prove that the four points with coordinates (-4,0) , (6,4), (5,0) and (0,-2) , are the vertices of a trapezium . Also find the equations of the diagonals of the trapezium and the acute angle at which the diagonals intersect.

Show that the points (3,0),(6,4) and (-1,3) are the vertices of a right angled isosceles triangle.

Without using the Pythagoras theorem, show that the points (4,4), (3, 5) and (-1, -1) are the vertices of a right angled triangle.

Show that the points (2a, 6a) (2a,4a) and (2a + sqrt3 a, 5a) are the vertices of an equilateral triangle of side 2a units.

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CHHAYA PUBLICATION-REVISION OF PREVIOUS TWO DIMENSIONAL COORDINATE GEOMETRY -EXERCISE 1 ( Short Type Questions )
  1. Prove that the points (2,-2) ,(8,4), (5,7) and (-1,1) are the vertices...

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  2. Show that the points (-2,-1),(5,4),((6,7) and (-1,2) are the vertices...

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  3. Prove that the four points (4,3),(6,4),(5,6) and (3,5) are the vertice...

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  4. Prove that the points (0,0),(0,10),(8,16)and (8,6)are the vertices of...

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  5. If the point (0,4) divides the line-segment joining the points (-4,10)...

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  6. The straight line joining the points (2, -2)and (4, 6) extended each w...

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  7. The coordinates of the vertex A of Delta ABC are (2,5), if the centroi...

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  8. The area of the trianglr formed by joining the points (2,7), (5,1) and...

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  9. Prove that the points (-4,-5) ,(9,8)and the mid-point of the line-seg...

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  10. Find the value of m for which the area of the triangle having vertice...

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  11. The vertices A,B and C of DeltaABC have coordinates (-3,-2),(2,-2) an...

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  12. Prove that the points (p,p^(2)),(q,q^(2))and(r,r^(2))(pner) can never ...

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  13. Find the area of the vertices A,B,C and D of the quadrilateral whose v...

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  14. The coordinates of the vertices A,B,C and D of the quadrilateral ABCD ...

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  15. What does the equation 3x^(2)+2xy+3y^(2)-18x-22y+50=0 become if the ax...

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  16. Find the point to which the origin should be shifted after a translat...

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  17. Verify that the area of the triangle with vertices (6,2), (-3,4) and ...

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  18. The distance of a point P from the striaght line x=-4 is equal to its...

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  19. A point P(x,y) moves in the xy - plane in such a way that its distance...

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  20. A point moves in a plane such that its distance from the point (2,3) e...

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