Home
Class 7
MATHS
Given that LP is a median of the DeltaLM...

Given that LP is a median of the `DeltaLMN`, explain where the point P lies.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question of where point P lies when LP is a median of triangle LMN, we can follow these steps: ### Step-by-Step Solution: 1. **Draw Triangle LMN**: - Begin by sketching triangle LMN. Label the vertices as L, M, and N. 2. **Identify the Median**: - A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. In this case, we are considering median LP, where L is one vertex of the triangle. 3. **Locate Midpoint of Side MN**: - To find point P, we need to determine the midpoint of side MN. Let's denote the midpoint of MN as point P. 4. **Draw the Median**: - Draw a line segment from vertex L to point P (the midpoint of MN). This line segment is the median LP. 5. **Understand the Property of the Median**: - By definition, a median divides the opposite side (MN) into two equal segments. Therefore, we have: - NP = PM - This means that point P is equidistant from points N and M. 6. **Conclusion about the Position of P**: - Since point P is the midpoint of side MN, it lies on line segment MN. Hence, point P is located on the line segment connecting points M and N. ### Final Statement: - Therefore, point P lies on side MN of triangle LMN. ---
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THE TRIANGLE AND ITS PROPERTIES

    ICSE|Exercise EXERCISE 12.1|7 Videos

  • THE TRIANGLE AND ITS PROPERTIES

    ICSE|Exercise EXERCISE 12.2|11 Videos

  • THE TRIANGLE AND ITS PROPERTIES

    ICSE|Exercise WARM UP EXERCISE|3 Videos

  • SYMMETRY

    ICSE|Exercise Exercise 19B|13 Videos

  • UNITARY METHOD

    ICSE|Exercise EXERCISE|16 Videos

Similar Questions

Explore conceptually related problems

If P is the point (2,1,6) find the point Q such that PQ is perpendicular to the plane x+y-2z=3 and the mid point of PQ lies on it.

Point (0,-7) lies

Knowledge Check

  • The coordinates of a point are (1,-3,3), the point lies in

    A
    (a)II octant
    B
    (b)VIII octant
    C
    (c)I octant
    D
    (d)IV octant

    • Similar Questions

    Explore conceptually related problems

    Point (-10,0) lies

    A vertical straight conductor carries a current vertically upwards. A point P lies to the east of it at a small distance and another point Q lies to the west at the same distance. The magnetic field at P is

    If the tangents at points P and Q of the parabola y^2 = 4ax intersect at R then prove that midpoint of R and M lies on the parabola where M is the midpoint of P and Q

    If the tangents at points P and Q of the parabola y^2 = 4ax intersect at R then prove that midpoint of R and M lies on the parabola where M is the midpoint of P and Q

    If P is the point (2,1,6) find the point Q such that PQ is perpendiculr to the plane in x+y-2z =3 and the mid point of PQ lies on it.

    Let A(2,0) and B(z) are two points on the circle |z|=2 . M(z') is the point on AB . If the point barz' lies on the median of the triangle OAB where O is origin, then arg(z') is

    In the given figure, AD is median of DeltaABC and E is any point on median AD. Prove that Area (DeltaABE) = Area (DeltaACE)

    Home
    Profile