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The points (-a,-b),(a,b),(0,0) and (a^(2...

The points `(-a,-b),(a,b),(0,0)` and `(a^(2),ab), a ne 0, b ne 0` are always

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Slope of `AB=b/a` slope `BC=b/a`
Slope of `CD=(b(a-1))/(a(a-1)) = b/a`
`therefore` A,B,C,D are collinear.
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PATHFINDER-RECTANGULAR CO-ORDINATES-QUESTION BANK
  1. Three points (0,0),(3,sqrt3),(3,lambda) form an equilateral triangle. ...

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  2. The point (22,23) divides the join of P(7,5) and Q externally in the r...

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  3. Find out in centre of the triangle formed by (1,2),(3,4) and (2,3).

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  4. The medians of a triangle meet at (0,-3) and two vertices are at (-1,4...

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  5. The points (-a,-b),(a,b),(0,0) and (a^(2),ab), a ne 0, b ne 0 are alwa...

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  6. Find the area of the triangle with vertices at the points (a,b+c),(b,c...

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  7. Find the area of the triangle with vertices at (-4,1),(1,2),(4,-3).

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  8. The points A(-2,3),B(3,4),C(x,y) form an equilateral triangle. Find x ...

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  9. Find the ratio in which the segment joining the points (5,6) and (2,-3...

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  10. Find the ratio in which the segment joining the points (5,6) and (2,-3...

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  11. Prove that the points A(-2,-1) B(1,0), C(4,3) and D(1,2) are the verti...

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  12. Find the equation of the lines joining the centroid G with the vertice...

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  13. Find the equation of the right bisector of the line joining (1,1) and ...

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  14. If the area of the quadrilateral whose angular points taken in order a...

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  15. Find the co-ordinates of the point which divided the join of P(5,-2) a...

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  16. Find the co-ordinates of the point which divided the join of P(5,-2) a...

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  17. Show that the quadrilateral with vertices A(3,2), B(0,5), C(-3,2), D(0...

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  18. A and B are points (3,4) and (5,-2), find the co-ordinate of the point...

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  19. Find the ratio in which the line joining (-5,1) and (1,-3) divides the...

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  20. Find the centre and radius of the circumcircle of the triangle whose v...

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