Answer:
The coordinate of C is (5,9)
Step-by-step explanation:
A, B and C are collinear and B is between A and C.
The ratio of AB to AC is 1:3
If A is at (2,-6) and B is at (3,-1)
AB:AC = 1:3
B is between A and C
AB:(AB+BC) = 1:(1+2)
Therefore, AB:BC = 1:2
Let the point C (a,b)
Using section formula:
[tex]x\rightarrow \dfrac{mx_2+nx_1}{m+n}[/tex]
[tex]y\rightarrow \dfrac{my_2+ny_1}{m+n}[/tex]
where,
[tex]m\rightarrow 1[/tex]
[tex]n\rightarrow 2[/tex]
[tex]x_1m\rightarrow 2[/tex]
[tex]y_1\rightarrow -6[/tex]
[tex]x\rightarrow 3[/tex]
[tex]y\rightarrow -1[/tex]
Substitute into formula and solve coordinate point C
[tex]3=\dfrac{1\cdot a+2\cdot 2}{1+2}[/tex]
[tex]3=\dfrac{a+4}{3}[/tex]
[tex]a=5[/tex]
[tex]-1=\dfrac{1\cdot b-6\cdot 2}{1+2}[/tex]
[tex]-1=\dfrac{b-12}{3}[/tex]
[tex]b=9[/tex]
Hence, The coordinate of C is (5,9)
