Respuesta :
Answer: C=(44,29).
Step-by-step explanation:
The given points are A = (-4 , -7) and B = (12 , 5).
It is given that Point B is 1/3 of the way from A to C.
AB:AC=1:3
AB:BC=AB:(AC-AB)=1:(3-1)=1:2
It means point B divides the line segment AC in 1:2.
Let coordinates of C are (a,b).
Section formula: If a point divides a line segment in m:n, then
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Using section formula, we get
[tex]B=\left(\dfrac{1(a)+2(-4)}{1+2},\dfrac{1(b)+2(-7)}{1+2}\right)[/tex]
[tex](12,5)=\left(\dfrac{a-8}{3},\dfrac{b-14}{3}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{a-8}{3}=12[/tex]
[tex]a-8=36[/tex]
[tex]a=36+8[/tex]
[tex]a=44[/tex]
[tex]\dfrac{b-14}{3}=5[/tex]
[tex]b-14=15[/tex]
[tex]b=15+14[/tex]
[tex]b=29[/tex]
Therefore, the coordinates of C are (44,29).
