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:
[tex]x_B-x_A = 3(x_C-x_B)\\y_B-y_A=3(y_X-y_B)[/tex]
where:
[tex](x_A,y_A)=(-7,3)[/tex] are the coordinates of point A
[tex](x_B,y_B)=(-1,0)[/tex] are the coordinates of point B
[tex](x_C,y_C)[/tex] are the coordinates of point C
Solving the equation for [tex]x_C[/tex],
[tex]x_C = x_B + \frac{x_B-x_A}{3}=-1+\frac{-1-(-7)}{3}=1[/tex]
Solving the equation for [tex]y_C[/tex],
[tex]y_C=y_B + \frac{y_B-y_A}{3}=0+\frac{0-3}{3}=-1[/tex]
So, the coordinates of point C are
[tex]C(-1,1)[/tex]
Learn more about how to divide segments:
brainly.com/question/3269852
brainly.com/question/11280112
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