Coordinates of point C: (1,-1)
Step-by-step explanation:
In this problem, A, B and C are collinear, and B is between A and C.
The ratio AB : BC is 3 : 1.
This means that we can write the following two equations:
![x_B-x_A = 3(x_C-x_B)\\y_B-y_A=3(y_X-y_B)](https://tex.z-dn.net/?f=x_B-x_A%20%3D%203%28x_C-x_B%29%5C%5Cy_B-y_A%3D3%28y_X-y_B%29)
where:
are the coordinates of point A
are the coordinates of point B
are the coordinates of point C
Solving the equation for
,
![x_C = x_B + \frac{x_B-x_A}{3}=-1+\frac{-1-(-7)}{3}=1](https://tex.z-dn.net/?f=x_C%20%3D%20x_B%20%2B%20%5Cfrac%7Bx_B-x_A%7D%7B3%7D%3D-1%2B%5Cfrac%7B-1-%28-7%29%7D%7B3%7D%3D1)
Solving the equation for
,
![y_C=y_B + \frac{y_B-y_A}{3}=0+\frac{0-3}{3}=-1](https://tex.z-dn.net/?f=y_C%3Dy_B%20%2B%20%5Cfrac%7By_B-y_A%7D%7B3%7D%3D0%2B%5Cfrac%7B0-3%7D%7B3%7D%3D-1)
So, the coordinates of point C are
Learn more about how to divide segments:
brainly.com/question/3269852
brainly.com/question/11280112
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