Home
Class 11
MATHS
Three vertices of a parallelogram ABCD a...

Three vertices of a parallelogram ABCD are `A (3, 1, 2)`, `B (1, 2, 4)`and `C ( 1, 1, 2)`. Find the coordinates of the fourth vertex.

Text Solution

AI Generated Solution

To find the coordinates of the fourth vertex \( D(x, y, z) \) of the parallelogram \( ABCD \) given the vertices \( A(3, 1, 2) \), \( B(1, 2, 4) \), and \( C(1, 1, 2) \), we can use the property that the diagonals of a parallelogram bisect each other. ### Step-by-Step Solution: 1. **Identify the Midpoints**: The diagonals \( AC \) and \( BD \) bisect each other. Therefore, the midpoint of diagonal \( AC \) must equal the midpoint of diagonal \( BD \). 2. **Calculate Midpoint of AC**: ...
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT ENGLISH|Exercise EXERCISE 12.2|5 Videos

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT ENGLISH|Exercise EXERCISE 12.3|5 Videos

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT ENGLISH|Exercise EXERCISE 12.1|4 Videos

  • CONIC SECTIONS

    NCERT ENGLISH|Exercise EXERCISE 11.1|15 Videos

  • LIMITS AND DERIVATIVES

    NCERT ENGLISH|Exercise EXERCISE 13.3|8 Videos

Similar Questions

Explore conceptually related problems

Three vertices of a parallelogram ABCD are A(3, 1, 2), B(0, 1, 5) and C(-1, 2, -3) Find the coordinates of the fourth vertex.

Three vertices of a parallelogram ABCD are A(3,-1,2),\ B(1,2,-4)a n d\ C(-1,1,2)dot Find the coordinates of the fourth vertex.

If the three vertices of a parallelogram ABCD are A(3, -1, 5), B(1, -2, -4) and C(0, 3, 0), then the coordinates of fourth vertex is

The three vertices of a parallelogram ABCD taken in order are A(3, -4), B(-1, -3) and C(-6, 2). Find the coordinates of the fourth vertex D.

The co-ordinates of the vertices of a parallelogram ABCD are A(-1,2,3), B(2, -4,1) and C(1,2,-1). Find the co-ordinates of its 4th vertex.

The coordinates of three consecutive vertices of a parallelogram are (1, 3), (-1, 2) and (2, 5). Then find the coordinates of the fourth vertex.

Three vertices of a parallelogram ABCD taken in order are A (3, 6), B (5, 10) and C (3, 2) find : (i) the coordinates of the fourth vertex D.

The three vertices of a parallelogram ABCD are A(-1,3,4), B(2,-1,3) and C(5,1,2). Find the co-ordinates of its 4th vertex D.

Three vertices of a parallelogram are (1, 2, 1), (2, 5, 6) and (1, 6, 0) Find the coordinates of the fourth vertex.

Three consective vertices of a parallelogram ABCD are A ( 6, -2 ,4) , B ( 2, 4,-8) and C (-2,2,4) . Find the condinates of the following