Question

In parallelogram ABCD, A = (6, 0), B = (12, −4) and C = (4, −4); then the cоordinates of vertex D are ______.

Options

• (2, 0)

• (−2, 0)

• (0, 2)

• (0, −2)

Answer 1

In parallelogram ABCD, A = (6, 0), B = (12, −4) and C = (4, −4); then the cоordinates of vertex D are (−2, 0).

Explanation:

Let co-ordinates of vertex D be (x, y).

We know that,

Diagonal of parallelogram bisect each other.

From figure,

O (a, b) is the mid-point of AC.

By mid-point formula,

Mid-point = `((x_1+x_2)/2, (y_1+y_2)/2)`

Substituting values we get :

(a, b) = `((6 + 4)/2, (0 + (-4))/2)`

= `(10/2, (-4)/2)`

= (5, −2).

From figure,

O is also the mid-point of BD.

∴ (5, −2) = `((12 + x)/2, (-4 + y)/2)`

⇒ `(12 + x)/2​ = 5 and (−4+y)/2 ​= −2`

⇒ 12 + x = 10 and −4 + y = −4

⇒ x = 10 − 12 and y = −4 + 4

⇒ x = −2 and y = 0

D = (−2, 0)