Question

L (-1,-1)

Answer 1

The answer is B) (2,-1).If you don’t believe me punch in the coordinates into a graphing calculator and then punch in (2,-1). It will give you a perfect parallelogram.

Answer 2

Answer:  The correct option is (B) (2, -1).

Step-by-step explanation:  Given that LMNO is a parallelogram where the co-ordinates of the vertices L,M and N are

L(-1,-1) ,  M(0,0)  and N(3,0).

We are to find the co-ordinates of the vertex O.

Let, (a, b) be the co-ordinates of the vertex O.

Since LMNO is parallelogram, so the opposite sides will be parallel.

That is, LM is parallel to NO. So, we have

$\textup{slope of LM}=\textup{slope of NO}\\\\\Rightarrow \dfrac{0-(-1)}{0-(-1)}=\dfrac{b-0}{a-3}\\\\\\\Rightarrow \dfrac{1}{1}=\dfrac{b}{a-3}\\\\\Rightarrow b=a-3\\\\\Rightarrow a=b+3~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and MN is parallel to OL. So,

$\textup{slope of MN}=\textup{slope of OL}\\\\\\\Rightarrow \dfrac{0-0}{3-0}=\dfrac{-1-b}{-1-a}\\\\\\\Rightarrow 0=\dfrac{b+1}{a+1}\\\\\\\Rightarrow b+1=0\\\\\Rightarrow b=-1.$

Therefore, from equation (i), we get

$a=-1+3=2.$

Thus, the co-ordinates of vertex O are (2, -1).

Option (B) is correct.