Question

A, B, and C are collinear, and B is between A and C. The ratio of AB to BC is 3 : 1.

Answer 1

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:

$x_B-x_A = 3(x_C-x_B)\\y_B-y_A=3(y_X-y_B)$

where:

$(x_A,y_A)=(-7,3)$ are the coordinates of point A

$(x_B,y_B)=(-1,0)$ are the coordinates of point B

$(x_C,y_C)$ are the coordinates of point C

Solving the equation for $x_C$,

$x_C = x_B + \frac{x_B-x_A}{3}=-1+\frac{-1-(-7)}{3}=1$

Solving the equation for $y_C$,

$y_C=y_B + \frac{y_B-y_A}{3}=0+\frac{0-3}{3}=-1$

So, the coordinates of point C are

$C(-1,1)$

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