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L (-1,-1)
M (0,0)
N (3,0)
Parallelogram LMNO has the coordinates shown.
Find the coordinates of point O.
A) (1,-1)
B) (2,-1)
C) (2,0)
D) (2,1)

Respuesta :

GabrielaBSF
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:  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

[tex]\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)[/tex]

and MN is parallel to OL. So,

[tex]\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.[/tex]

Therefore, from equation (i), we get

[tex]a=-1+3=2.[/tex]

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

Option (B) is correct.

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