Question

$\large\mathbf{HEY\: QUESTION❤}$



Three vertices of a parallelogram taken in order are (-1, 0), (3, 1) and (2, 2) respectively. Find the coordinates of fourth vertex.​

Answer 1

Answer:

Hope it's helpful!! Done in steps

Answer 2

Answer:

The fourth vertex of the parallelogram is (-2, 1)

Step-by-step explanation:

Let A(-1, 0), B(3, 1), C(2, 2) and D(x, y) be the vertices of a parallelogram ABCD taken in order. Since, the diagonals of a parallelogram bisect each other.

∴ Coordinates of the mid-point of AC=Coordinates of the mid-point of BD

$⇒ ( \frac{ - 1 + 2 \: ,}{2} \frac{0 + 2}{2} ) =$

$( \frac{3 + x}{2}, \frac{1 + y}{2} )$

$⇒( \frac{1}{2},1 ) = ( \frac{3 + x}{2} , \frac{y + 1}{2} )$

$⇒ \frac{3 + x}{2} = \frac{1}{2} \: and \: \frac{y + 1}{2} = 1$

$⇒x=−2 \: and \: y \: =1</p><p></p><p>$

Hence, the fourth vertex of the parallelogram is (-2, 1)