Question

If the three vertices of a parallelogram are (a+b,a-2) , (2a+b,2a-2) , (a-b,a+2) , then find the fourth vertex
a) (b,2)
b) (-b,2)
c) (b,-2)
d) (-b,-2)​

Answer 1

Answer:

d

Step-by-step explanation:

Let ABCD be a parallelogram.

Let A(a+b,a−b),B(2a+b,2a−b) and C(a−b,a+b). We have to find co-ordinates of the fourth vertex.

Let fourth vertex be D(x,y)

Since, ABCD is a parallelogram, the diagonals bisect each other.

∴ The mid-point of the diagonals of the parallelogram will coincide.

Mid - point formula,

P(x,y)=(

2

x

1

+x

2

,

2

y

1

+y

2

)

The mid-point of the diagonals of the parallelogram will coincide.

Si, co-ordinate of mid-point of AC= Co-ordinate of mid-point of BD

∴ (

2

a+b+a−b

,

2

a−b+a+b

)=(

2

2a+b+x

,

2

2a−b+y

)

⇒ (a,a)=(

2

2a+b+x

,

2

2a−b+y

)

Now, equate he individual terms to get the unknown value. So we get,

⇒ x=−b

⇒ y=b

∴ The fourth vertex is D(−b,b)