Home
Class 10
MATHS
x1, x2 , x3 and y1, y2, y3 …….. are arit...

`x_1, x_2 , x_3` and `y_1, y_2, y_3 ……..` are arithmetic sequences. Prove that all points with coordinates in the sequence `(x_1, y_1),(x_2, y_2),(x_3, y_3), ………...` of number pairs are on the same line.

Promotional Banner

Topper's Solved these Questions

  • COORDINATES

    V PUBLICATION|Exercise QUESTION BANK|56 Videos

  • MATHEMATICS OF CHANCE

    V PUBLICATION|Exercise QUESTION BANK|62 Videos

Similar Questions

Explore conceptually related problems

What are the coordinates of the centroid of the triangle with vertices (x_1,y_1) (x_2,y_2) and (x_3,y_3)

If x_(1) , x _(2), x _(3) as well as y _(1), y _(2) , y _(3) are in GP with the same common ratio, then the point (x _(1) , y _(1)) , (x _(2) , y _(2)) and (x_(3) , y _(3)):

Write the coordinate of the centroid of the triangle whose vertices are (x_1,y_1,z_1) , (x_2,y_2,z_2) and (x_3,y_3,z_3)

Find the slope of the tangent to curve y=x^3-x+1 at the point whose x-coordinate is 2.

If A(x_1, y_1), B(x_2, y_2) and C(x_3, y_3) are vertices of an equilateral triangle whose each side is equal to 'a', then prove that, |[x_1, y_1, 2 ],[ x_2, y_2, 2],[ x_3, y_3, 2]|^2=3 a^4

(b)The coordinates of the point R which divides the line segment joining P(x1,y1,z1) and Q(x2,y2,z2) internally in the ratio m:n are given by…………

The figure shows a parallelogram with the coordinates of its vertices: Prove that x_1+x_3=x_2+x_4andy_1+y_3=y_2+y_4

Consider the curve 2y=3-x^2 Find the slope of the tangent to this curve at (x_1,y_1) .

Let |A|=|[x_1, x_2, x_3],[ y_1, y_2, y_3],[ z_1 , z_2, z_3]| .Expand |A| along the first row and along the first column. Comment on the two results.

For what values of x and y are the following matrices equal ? A=[(2x+1,3y),(0,y^(2)-5y)], B=[(x+3,y^(2)+2),(0,-6)]

V PUBLICATION-GEOMETRY AND ALGEBRA-QUESTION BANK
  1. Prove that the points '(1,3),(2,5)' '(3,7)' are on the same line.

    Text Solution

    |

  2. Find the coordinates of two more points on the line joining '(-1,4)' a...

    Text Solution

    |

  3. x1, x2 , x3 and y1, y2, y3 …….. are arithmetic sequences. Prove that a...

    Text Solution

    |

  4. Prove that if the points (x1, y1),(x2, y2), (x3, y3) are on a single l...

    Text Solution

    |

  5. Find the equation of the line joining (1,2) and (2,4), For points on t...

    Text Solution

    |

  6. Find the equation of the line joining (-1,3) and (2,5).Prove that if t...

    Text Solution

    |

  7. Prove that whatever number we take as x,the point (x,2x+3) is a point ...

    Text Solution

    |

  8. In the picture below, the x coordinate of a point on the slanted (blue...

    Text Solution

    |

  9. In the picture here, 'ABCD' 'is a square. Prove that for any point on ...

    Text Solution

    |

  10. Prove that for any point on the line intersecting the axes in the pict...

    Text Solution

    |

  11. Find the equation of the circle with centre at the origin and radius '...

    Text Solution

    |

  12. Prove that if '(x, y)' be a point on the circle with the line joining ...

    Text Solution

    |

  13. What is the equation of the circle shown below? '(##VPUTTTMATXP02C09E0...

    Text Solution

    |

  14. What are the coordinates of the centroid of the triangle with vertices...

    Text Solution

    |

  15. We have seen that the points (3,5),(6,7),(9,9) are points on the same ...

    Text Solution

    |

  16. Prove that the quadrilateral formed by joining the points '(-1,-1),(6,...

    Text Solution

    |

  17. (7,10)' is a point on the circle centred at '(1,2) .' Find the length ...

    Text Solution

    |

  18. If a circle is drawn with centre as origin and radius 2, then how many...

    Text Solution

    |

  19. Prove that for all points on the line joining the origin and the point...

    Text Solution

    |

  20. What is the equation of the line joining the points '(1,3),(2,7) ?' Pr...

    Text Solution

    |