Question

if (-1,2) , (2,-1) and (3,1) are any three vertices of a parallelogram , then the fourth vertex (a,b) will be such that
a) a = 2 b = 0 b) a = -2 b = 0 c) a = -2 b = 6 d) a = 6 b = -2

it is a multiple choice answer

Answer 1

The fourth vertex is (0, 4).

Step-by-step explanation:

Given,

Let the four vertices of a parallelogram = A( - 1, 2), B(2, - 1), C(3, 1) and D(a, b)

To find, the fourth vertex (a, b)=

We know,

The diagonals of the parallelogram bisect each other.

∴ Mid point of diagonal BD = Mid Point of diagonal AC

Mid point of diagonal BD = $(\dfrac{2+a}{2},\dfrac{-1+b}{2})$

Also,

Mid Point of diagonal AC = $(\dfrac{-1+3}{2},\dfrac{2+1}{2})$

= $(\dfrac{2}{2},\dfrac{3}{2})$

∴ $\dfrac{2+a}{2} = \dfrac{2}{2}$

⇒ 2 + a = 2

⇒ a = 2 - 2 = 0

And, $\dfrac{-1+b}{2}=\dfrac{3}{2}$

⇒ b = 3 + 1 = 4

There are no option match.

Thus, the fourth vertex is (0, 4).

Answer 2

Step-by-step explanation:

guys here there no option like that so you can change the option

AND PLS MARK ME AS BRAINLIST

AND IN TEXT YOU WILL NOT ABLE TO UNDERSTAND SO I PUT THE IMAGE

SORRY FOR HANDWRINTING