Question

Find the 4^th vertex of a parallelogram if three vertices taken in order are (−5, −5) (2, −3), and (4, 4).

Answer 1

Here, let,

• A = (−5, −5),
• B = (2, −3),
• C = (4, 4)

In a parallelogram ABCD (vertices in order), D = A + (C − B),

⇒ C − B = (4, 4) − (2, −3)

= (4 − 2, 4 − (−3))

= (2, 7)

⇒ A + D = (−5, −5) + (2, 7)

= (−5 + 2, −5 + 7)

= (−3, 2)

Hence, the fourth vertex is (−3, 2).