Answer:
The coordinates of the midpoint of LN are ![(-2\frac{1}{2},4\frac{1}{2})](https://tex.z-dn.net/?f=%28-2%5Cfrac%7B1%7D%7B2%7D%2C4%5Cfrac%7B1%7D%7B2%7D%29)
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 ![x=\frac{x_{1}+x_{2}}{2},y=\frac{y_{1}+y_{2}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7Bx_%7B1%7D%2Bx_%7B2%7D%7D%7B2%7D%2Cy%3D%5Cfrac%7By_%7B1%7D%2By_%7B2%7D%7D%7B2%7D)
∵ 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)
∵ ![x=\frac{-6+1}{2}=\frac{-5}{2}=-2\frac{1}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%2B1%7D%7B2%7D%3D%5Cfrac%7B-5%7D%7B2%7D%3D-2%5Cfrac%7B1%7D%7B2%7D)
∵ ![y=\frac{1+8}{2}=\frac{9}{4}=4\frac{1}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%2B8%7D%7B2%7D%3D%5Cfrac%7B9%7D%7B4%7D%3D4%5Cfrac%7B1%7D%7B2%7D)
∴ The coordinates of the midpoint are ![(-2\frac{1}{2},4\frac{1}{2})](https://tex.z-dn.net/?f=%28-2%5Cfrac%7B1%7D%7B2%7D%2C4%5Cfrac%7B1%7D%7B2%7D%29)
* The coordinates of the midpoint of LN are ![(-2\frac{1}{2},4\frac{1}{2})](https://tex.z-dn.net/?f=%28-2%5Cfrac%7B1%7D%7B2%7D%2C4%5Cfrac%7B1%7D%7B2%7D%29)