Home
Class 10
MATHS
A(8, -6), B(-4, 2) and C(0, -10) are ver...

A(8, -6), B(-4, 2) and C(0, -10) are vertices of a triangle ABC. If P is the mid-point of AB and Q is the mid-point of AC, use co-ordinate geometry to show that PQ is parallel to BC. Give a special name to quadrilateral PBCQ. 

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • EQUATION OF A LINE

    ICSE|Exercise EXERCISE 14(D)|41 Videos

  • CYLINDER, CONE AND SPHERE

    ICSE|Exercise EXERCISE 20 (G)|23 Videos

  • FACTORISATION

    ICSE|Exercise M.C.Q(Competency Based Questions )|15 Videos

Similar Questions

Explore conceptually related problems

A (5, 3), B (-1, 1) and C (7, -3) are the vertices of triangle ABC. If L is the mid-point of AB and M is the mid-point of AC, show that : LM = (1)/(2) BC .

A(6,1) , B (8,2) and C (9,4) are three vertices of a parallelogram ABCD . If E is the mid - point of DC , then find the area of triangle ADE.

A (8,0), B (0,-8) and C (-16, 0) are the vertices of a triangle ABC. If P is in AB and Q is in AC such that AP : PB = AQ : QC =3:5, show that 8PQ = 3 BC.

In triangle ABC, M is mid-point of AB, N is mid-point of AC and D is any point in base BC. Use Intercept Theorem to show that MN bisects AD.

A(-8, O), B(0, 16) and C(0, 0) are the vertices of a triangle ABC. Point P lies on AB and Q lies on AC such that AP : PB = 3 : 5 and AQ: QC = 3:5. Show that : PQ = (3)/(8) BC.

In triangle ABC, P is mid-point of AB and Q is mid-point of AC. If AB = 9.6 cm, BC = 11 cm and AC = 11.2 , find the perimeter of the trapezium PBCQ.

A (2, 5), B (1, 0), C (-4, 3) and D (-3, 8) are the vertices of quadrilateral ABCD. Find the co-ordinates of the mid-points of AC and BD. Give a special name to the quadrilateral.

A (-4, 2), B(0, 2) and C(-2,-4) are vertices of a triangle ABC. P, Q and R are mid-points of sides BC, CA and AB respectively. Show that the centroid of Delta PQR is the same as the centroid of Delta ABC.

In triangle ABC, D and E are mid-points of sides AB and BC respectively. Also, F is a point in side AC so that DF is parallel to BC (i) Prove that DBEF is a parallelogram.

In triangle ABC, D is mid-point of AB and P is any point on BC. If CQ parallel to PD meets AB at Q, prove that: 2 xx " area " (Delta BPQ) = " area "(Delta ABC)

ICSE-EQUATION OF A LINE-EXERCISE 14(E)
  1. From the given figure, find : the equation of the line through A ...

    Text Solution

    |

  2. P(3, 4), Q(7, -2) and R(-2, -1) are the vertices of triangle PQR. Writ...

    Text Solution

    |

  3. A(8, -6), B(-4, 2) and C(0, -10) are vertices of a triangle ABC. If P ...

    Text Solution

    |

  4. In the given figure, line APB meets the x-axis at point A and y-axis a...

    Text Solution

    |

  5. A line AB meets the x-axis at point A and y-axis at point B. The point...

    Text Solution

    |

  6. A line intersects x-axis at point (-2, 0) and cuts off an intercept of...

    Text Solution

    |

  7. Find the equation of a line passing through the point (2, 3) and havin...

    Text Solution

    |

  8. The given figure (not drawn to scale) shows two straight lines AB and ...

    Text Solution

    |

  9. Write down the equation of the line whose gradient is 3/2 and which pa...

    Text Solution

    |

  10. The ordinate of a point lying on the line joining the points (6, 4) an...

    Text Solution

    |

  11. Point A and B have co-ordinates (7, -3) and (1,9) respectively. Find :...

    Text Solution

    |

  12. Point A and B have co-ordinates (7, -3) and (1,9) respectively. Find :...

    Text Solution

    |

  13. Point A and B have co-ordinates (7, -3) and (1,9) respectively. Find :...

    Text Solution

    |

  14. A and B are two points on the x-axis and y-axis respectively. P(2, -3)...

    Text Solution

    |

  15. A and B are two points on the x-axis and y-axis respectively. P(2, -3)...

    Text Solution

    |

  16. A and B are two points on the x-axis and y-axis respectively. P(2, -3)...

    Text Solution

    |

  17. The equation of a line is 3x + 4y - 7 = 0. Find: the slope of the li...

    Text Solution

    |

  18. The equation of a line is 3x + 4y - 7 = 0. Find: the equation of a l...

    Text Solution

    |

  19. ABCD is a parallelogram where A(x, y), B(5, 8), C(4, 7) and D(2, -4). ...

    Text Solution

    |

  20. ABCD is a parallelogram where A (x, y), B (5, 8), C (4, 7) and D 2, -4...

    Text Solution

    |