Respuesta :
Answer:
The coordinates of point O are (2,-1).
Step-by-step explanation:
The opposites sides of parallelogram are parallel to each other and the slopes of parallel lines are equal.
Slope formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let the coordinates of point O be (x,y).
The sides LM and NO are parallel to each other. So, the slope of LM is equal to slope of LM.
[tex]m_{LM}=m_{NO}[/tex]
[tex]\frac{0-(-1)}{0-(-1)}=\frac{0-b}{3-a}[/tex]
[tex]\frac{1}{1}=\frac{-b}{3-a}[/tex]
[tex]3-a=-b[/tex]
[tex]3=a-b[/tex] .... (1)
The sides LO and MN are parallel to each other. SO, the slope of LO is equal to slope of MN.
[tex]m_{LO}=m_{MN}[/tex]
[tex]\frac{b-(-1)}{a-(-1)}=\frac{0-0}{3-0}[/tex]
[tex]\frac{b+1}{a+1}=0[/tex]
[tex]b+1=0[/tex]
[tex]b=-1[/tex]
Therefore the value of b is -1.
Put b=-1 in equation 1.
[tex]3=a-(-1)[/tex]
[tex]3=a+1[/tex]
[tex]a=2[/tex]
The value of a is 2. Therefore the coordinates of point O are (2,-1).
