Answer:
The answer is (-4, 15/2)
Step-by-step explanation:
Let the Boone be x, Winston-Salem be y, Raleigh be z and Burlington be m.
We are given that Winston-Salem is halfway between Boone and Raleigh. Burlington is halfway between Winston- Salem and Raleigh.
If Boone is located at the coordinates (-1,3) and Raleigh is at (-5, 9).
We will use Midpoint Formula
![( \frac{x _{1} + x _{2}}{2} , \frac{y _{1} + y _{2}}{2} ) \\](https://tex.z-dn.net/?f=%28%20%5Cfrac%7Bx%20_%7B1%7D%20%2B%20x%20_%7B2%7D%7D%7B2%7D%20%2C%20%5Cfrac%7By%20_%7B1%7D%20%2B%20y%20_%7B2%7D%7D%7B2%7D%20%29%20%5C%5C%20)
Where,
x₁ = (-1) and x₂ = (-5)
y₁ = 3 and y₂ = 9
Now, We will find Co-ordinates of y i.e., Winston-Salem.
So,
![( \frac{( - 1) + ( - 5)}{2} , \frac{3 + 9}{2} ) \\](https://tex.z-dn.net/?f=%20%28%20%5Cfrac%7B%28%20-%201%29%20%2B%20%28%20-%205%29%7D%7B2%7D%20%2C%20%5Cfrac%7B3%20%2B%209%7D%7B2%7D%20%29%20%5C%5C%20)
![( \frac{( - 1 - 5)}{2} , \frac{12}{2} ) \\](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%28%20-%201%20-%205%29%7D%7B2%7D%20%2C%20%5Cfrac%7B12%7D%7B2%7D%20%29%20%5C%5C%20)
![( \frac{ - 6}{2} , \frac{12}{2} ) \\](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%20-%206%7D%7B2%7D%20%2C%20%5Cfrac%7B12%7D%7B2%7D%20%29%20%5C%5C%20)
![( - 3,6)](https://tex.z-dn.net/?f=%28%20-%203%2C6%29)
Here, The coordinates of y i.e., Winston-Salem is (-3, 6).
Now, We will find Co-ordinates of m i.e., Burlington.
So,
Again, Using of Midpoint Formula;
Where,
x₁ = (-3) and x₂ = (-5)
y₁ = 6 and y₂ = 9
So,
![( \frac{( - 3) + ( - 5)}{2} , \frac{6 + 9}{2} ) \\](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%28%20-%203%29%20%2B%20%28%20-%205%29%7D%7B2%7D%20%2C%20%5Cfrac%7B6%20%2B%209%7D%7B2%7D%20%29%20%5C%5C%20)
![( \frac{( - 3 - 5)}{2} , \frac{15}{2} ) \\](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%28%20-%203%20-%205%29%7D%7B2%7D%20%2C%20%5Cfrac%7B15%7D%7B2%7D%20%29%20%5C%5C%20)
![( \frac{( -8)}{2} , \frac{15}{2} ) \\](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%28%20-8%29%7D%7B2%7D%20%2C%20%5Cfrac%7B15%7D%7B2%7D%20%29%20%5C%5C%20)
![( - 4 , \frac{15}{2} ) \\](https://tex.z-dn.net/?f=%28%20-%204%20%20%2C%20%5Cfrac%7B15%7D%7B2%7D%20%29%20%5C%5C%20)
Thus, The coordinates of Burlington is (-4, 15/2).