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Cartesian Coordinate System

ABCD is a qua...

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ABCD is a quadrilateral the p(3,7) and q(7,3) are coordinates of midpoints of diagonals AC and BD respectively then find the corrdinates of midpoint of pq.

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M

N

are the midpoints of the diagonals

A C

B D

respectively of quadrilateral

A B C D

¯ ¯¯¯¯¯¯ ¯ A B + ¯ ¯¯¯¯¯¯¯ ¯ A D + ¯ ¯¯¯¯¯¯ ¯ C B + ¯ ¯¯¯¯¯¯¯ ¯ C D =

................

Q. If P and Q are the midpoints of the diagonals AC and BD respectively of a quadrilateral ABCD, prove that

¯ ¯¯¯¯¯¯ ¯ A B + ¯ ¯¯¯¯¯¯¯ ¯ A D + ¯ ¯¯¯¯¯¯ ¯ C B + ¯ ¯¯¯¯¯¯¯ ¯ C D = 4 ¯ ¯¯¯¯¯¯ ¯ P Q

Q. If ABCD is a quadrilateral and E and F are the midpoints of AC and BD respectively, prove that

\to A B + \to A D + \to C B + \to C D = 4 \to E F

In the given figure, ABCD is a trapezium. M and N are midpoints of diagonals AC and BD respectively. Which of the following is true?

Q. The midpoints of the sides AB, BC, CD and DA of a quadrilateral ABCD are joined to form a quadrilateral. If AC = BD and AC ⊥ BD then prove that the quadrilateral formed is a square.

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