Using proportions, it is found that the coordinates of Q are given as follows: (3.5, 1.25).
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Since the point Q partitions the segment AC in a 3:1 ratio, we have that the equation is:
![Q - A = \frac{3}{4}(C - A)](https://tex.z-dn.net/?f=Q%20-%20A%20%3D%20%5Cfrac%7B3%7D%7B4%7D%28C%20-%20A%29)
For the x-coordinate, we have that:
![Q - A = \frac{3}{4}(C - A)](https://tex.z-dn.net/?f=Q%20-%20A%20%3D%20%5Cfrac%7B3%7D%7B4%7D%28C%20-%20A%29)
![x - 2 = \frac{3}{4}(4 - 2)](https://tex.z-dn.net/?f=x%20-%202%20%3D%20%5Cfrac%7B3%7D%7B4%7D%284%20-%202%29)
![x - 2 = \frac{3}{2}](https://tex.z-dn.net/?f=x%20-%202%20%3D%20%5Cfrac%7B3%7D%7B2%7D)
x = 3.5
For the y-coordinate, we have that:
![Q - A = \frac{3}{4}(C - A)](https://tex.z-dn.net/?f=Q%20-%20A%20%3D%20%5Cfrac%7B3%7D%7B4%7D%28C%20-%20A%29)
![y + 1 = \frac{3}{4}(2 - (-1))](https://tex.z-dn.net/?f=y%20%2B%201%20%3D%20%5Cfrac%7B3%7D%7B4%7D%282%20-%20%28-1%29%29)
![y + 1 = \frac{9}{4}](https://tex.z-dn.net/?f=y%20%2B%201%20%3D%20%5Cfrac%7B9%7D%7B4%7D)
y = 1.25.
The coordinates of Q are given as follows: (3.5, 1.25).
More can be learned about proportions at brainly.com/question/24372153
#SPJ1