Home
Class 12
MATHS
ABCD is a quadrilateral. E is the point ...

ABCD is a quadrilateral. E is the point of intersection of the line joining the mid-points of the oppsote sides. If O is any point and OA+OB+OC+OD=xOE, then x is equal to

A

3

B

9

C

7

D

4

Text Solution

Verified by Experts

The correct Answer is:
D

let `OA=a,OB=b,OC=c`
and OD=d
Therefore, `OA+OB+OC+OD`
`=a+b+c+d`
P, the mid-point of `AB`, is `(a+b)/(2)`
Q, the mid-point of Cd, is `(c+d)/(2)`.
therefore, the mid-point of PQ is `(a+b+c+d)/(4)`
Similarly, the mid point of RS is `(a+b+c+d)/(4)`
i.e., `OE=(a+b+c+d)/4`.
`implies x=4`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the mid point of the line segment joining the points (3, 0) and (-1, 4)

The line segment joining the mid-points of any two sides of a triangle in parallel to the third side and equal to half of it.

If P and Q are the middle points of the sides BC and CD of the parallelogram ABCD, then AP+AQ is equal to

Prove that line segment joining mid points of the two sides of the triangle is parallel to third side.

The length of projection of the line segmet joining the points (1, 0, -1) and (-1, 2, 2) on the plane x+3y-5z=6 is equal to

A side of an equillateral triangle is 20cm long. A second equilateral triangle is inscribed in it by joining the mid-points of the sides of the first triangle. The progress is continued as shown in the accompanying diagram. Find the perimeter of the sixth inscribed equilateral triangle.

.......... of the following is the line joining the point of intersection y-x + 7=0 and y+ 2x - 2=0 and origin.

Using therem 6.2, prove that the line joining the mid-point of any two sides of a triangle is parallel to third side. (Recall that you have done it in class IX).

The lines joining the origin to the points of intersection of 2x^2 + 3xy -4x +1 = 0 and 3x + y=.1 given by

The angle between the pair of straight lines formed by joining the points of intersection of x^2+y^2=4 and y=3x+c to the origin is a right angle. Then c^2 is equal to