Answer:
The coordinates of the midpoint of LN are [tex](-2\frac{1}{2},4\frac{1}{2})[/tex]
answer (4)
Step-by-step explanation:
* Lets explain how to find the midpoint of a line
- The coordinates of the midpoint of a line whose endpoints are (x1 , y1)
and (x2 , y2) are [tex]x=\frac{x_{1}+x_{2}}{2},y=\frac{y_{1}+y_{2}}{2}[/tex]
∵ LMNO is a square
∵ The coordinates of point L are (-6 , 1)
∵ The coordinates of point N are (1 , 8)
- Let the coordinates of point L are (x1 , y1) , the coordinates of point
N are (x2 , y2) and the coordinates of the midpoint of LN are (x , y)
∴ x1 = -6 , x2 = 1 and y1 = 1 , y2 = 8
- Use the rule of the midpoint above to find the midpoint (x , y)
∵ [tex]x=\frac{-6+1}{2}=\frac{-5}{2}=-2\frac{1}{2}[/tex]
∵ [tex]y=\frac{1+8}{2}=\frac{9}{4}=4\frac{1}{2}[/tex]
∴ The coordinates of the midpoint are [tex](-2\frac{1}{2},4\frac{1}{2})[/tex]
* The coordinates of the midpoint of LN are [tex](-2\frac{1}{2},4\frac{1}{2})[/tex]
