Respuesta :
Answer:
The coordinates of point C are (0,-3).
Step-by-step explanation:
It is given that A, B, and C are collinear and B is between A and C.
The ratio of AB to AC is 3:4. Let length of AB and AC be 3x and 4x respectively.
[tex]AC=AB+BC[/tex]
[tex]4x=3x+BC[/tex]
[tex]x=BC[/tex]
[tex]\frac{AB}{BC}=\frac{3x}{x}=3:1[/tex].
Therefore, AB to BC is 3:1.
The given ordered pairs are A(-8,1) and B(-2,-2).
Let as assume that the coordinate of C is (a,b).
Section formula:
If a point divides a line segment in m:n whose end points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the coordinates of that point are
[tex](\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]
Point B divided the line AC is 3:1. Using section formula we get
[tex]B=(\frac{(3)(a)+(1)(-8)}{3+1},\frac{(3)(b)+(1)(1)}{(3)+(1)})[/tex]
[tex]B=(\frac{3a-8}{4},\frac{3b+1}{4})[/tex]
The coordinates of B are (-2,-2).
[tex](-2,-2)=(\frac{3a-8}{4},\frac{3b+1}{4})[/tex]
On comparing both sides.
[tex]-2=\frac{3a-8}{4}[/tex]
[tex]-8=3a-8[/tex]
[tex]0=3a[/tex]
[tex]a=0[/tex]
The value of a is 0.
[tex]-2=\frac{3b+1}{4}[/tex]
[tex]-8=3b+1[/tex]
[tex]-9=3b[/tex]
[tex]-3=b[/tex]
The value of b is -3.
Therefore the coordinates of point C are (0,-3).
