Question

The three vertices of a parallelogram taken in order are (0, 1), (−1, −2), and (2, 1). The coordinates of fourth vertex are ______.

विकल्प

• (2, 3)

• (3, 4)

• (4, 3)

• (3, 2)

Answer 1

The three vertices of a parallelogram taken in order are (0, 1), (−1, −2), and (2, 1). The coordinates of fourth vertex are (3, 4).

Explanation:

In a parallelogram, the diagonals bisect each other,

So the midpoint of AC:

= `((0 + 2)/2, (1 + 1)/2)`

= (1, 1)

Set this equal to the midpoint of BD:

= `((-1+x)/2, (-2+y)/2)`

(Multiplying both sides by 2)

= (−1 + x = 2), (−2 + y = 2)

∴ x = 3, y = 4