Question

verify that the diagonals of the rectangle with vertices p(-1,4) Q (-2,1) R (4,-1) and S (5,2) bisect each other

Answer 1

Step-by-step explanation:

ΔADC and ΔBDC are right angled triangle with AD and BC are hypotenuse.

AC2=AB2+DC2

AC2=(5−2)2+(6+1)2=9+48=58 sq.unit

BD2=DC2+CB2

BD2=(5−2)2+(−1−6)2=9+49=58 sq.unit

Hence, both the diagonals are equal in length.

In ΔABO and ΔCDO

Since, ∠OAB=∠OCD, ∠OBA=∠ODC (Both are alternate interior angles of parallel lines)

and AB=CD

Therefore ΔABO≅ΔCDO

⇒AO=CO and BO=DO

Therefore, Both diaginals bisects each other.

Answer 2

Answer:

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