Question

Show that the points A(-6, -5), B(5,-5), C(5, -8) and D(-6, -8) are vertices
a rectangle. Find the lengths of its diagonals. Are they equal?

Answer 1

Answer:

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

AC

2

=AB

2

+DC

2

AC

2

=(5−2)

2

+(6+1)

2

=9+48=58 sq.unit

BD

2

=DC

2

+CB

2

BD

2

=(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.