Question

Find the 4^th vertex of a parallelogram if three vertices taken in order are (1, −1), (−2, 2), and (4, 8).

Answer 1

Here, let;

• A = (1, −1),
• B = (−2, 2),
• C = (4, 8)

For a parallelogram with vertices A, B, C, D taken in order, the fourth vertex is D = A + C − B,

Computing:

⇒ D_x = A + C − B

= 1 + 4 − (−2)

∴ D_x = 7

⇒ D_y = A + C − B

= −1 + 8 − 2

∴ D_y = 5

Hence, the fourth vertex is (7, 5).