Question

A (14,-2), B (6,-2) and D(8,2) are the three vertices of a parallelogram ABCD. Find the coordinates of the fourth vertex C.

Answer 1

Step-by-step explanation:

we must use midpoint formula

Answer 2

The coordinates of the fourth vertex C = (0, 2)

Step-by-step explanation:

Let the coordinates of the fourth vertex is C(x, y).

The given hree vertices of a parallelogram ABCD are A (14, - 2), B (6, - 2) and D(8 , 2).

To find, the coordinates of the fourth vertex C = ?

∴ Diagonal of AC = Diagonal of BD

Diagonal of AC = ($\dfrac{14+x}{2}, \dfrac{-2+y}{2}$)

Also,

Diagonal of BD = ($\dfrac{6+8}{2}, \dfrac{-2+2}{2}$)

∴$\dfrac{14+x}{2}=\dfrac{6+8}{2}$

⇒ 14 + x = 14

⇒ x = 14 - 14 = 0

Also,

$\dfrac{-2+y}{2}=\dfrac{-2+2}{2}$

⇒ - 2 + y = - 2 + 2

⇒ y = 2

∴ The coordinates of the fourth vertex C = (0, 2)