Question

The three vertices of a rectangle are (-1,0).
(3,1) and (2.2) respectively then fourth is
A) (12)
B) (-2,1
C) (2.4
D) (1 ,3)​

Answer 1

$option \: (b) \: is \: correct \: one \\ \\ = ( - 2, 1)$

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

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

Answer 2

Answer:

B (-2,1)

kritika's sis ans is correct

hope it is useful to u