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If the point (a,b), (a',b') and (a-a',b-b') are collinear, then prove that ab' = a'b.

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CALCUTTA BOOK HOUSE-AREA OF TRIANGLES-Long-answer type questions :
  1. For what value of k the points (1,-1), (2,-1) and (k,-1) are collinear...

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  2. Prove that the line segment obtained by joining the points (1,2) and (...

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  3. Prove that the mid-point of the line segment obtained by joining the p...

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  4. Find the area of the quadrilateral formed by the points (1,4), (-2,1),...

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  5. The coordinates of A, B and C are (3,4), (-4,3) and (8,-6) respectivel...

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  6. The coordinates of A of the DeltaABC are (2,5) and the coordinates of ...

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  7. A (-1,5), B (3,1) and C (5,7) are the vertices of the DeltaABC. D,E an...

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  8. The coordinates of the points A,B,C,D are (0,-1),(-1,2),(15,2) and (4,...

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

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  10. Find the area of the triangle with vertices at (a,(1)/(a)),(b,(1)/(b))...

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  11. Locate the number 1.4 on the number line by the method of successive ...

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  12. The coordinates of A, B and C of the DeltaABC are (3,1), (9,7) and (-3...

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  13. If the coordinates of A, B, C and D are (6,3), (-3,5), (4,-2) and (x,3...

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  14. If the point (a,b), (a',b') and (a-a',b-b') are collinear, then prove ...

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  15. Prove that (a,b + c), (b,a + c) and (c, a + b) are collinear.

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  16. If P (-2,3), Q (4,-5) and R (-3,1) are the three consecutive vertices ...

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  17. Four vertices of a quadrilateral are (-5,-5), (2,-4), (3,2) and (-2,3)...

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  18. Four vertices of a quadrilateral are (1,2), (-5,6), (7,-4) and (k,-2) ...

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  19. Four vertices of a quadrilateral are A (-1,6) B (-2.-4), C (3,-2) and ...

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