Question

again i hope you can see the picture if you can’t let me know but if you can please help!

Answer 1

Answer:

The point that divides the line AB in the ration 2 : 1 is $C(-2,2)$

Step-by-step explanation:

Given:

Point $A(-8, 4)$ and point $B(10, -2)$

Point $C(x,y)$ lies in between of AB such that $AC : CB = 2 : 1$

Using section formula which says that, when a point P divided a line AB in the ratio $m : n$, then the co-ordinates of the point P are:

$x=\frac{mx_2+nx_1}{m+n}\\y=\frac{my_2+ny_1}{m+n}$

Here, $(x_1,y_1)=(-8,4),(x_2,y_2)=(10,-2),m=2,n=1$

Therefore, the $x$ and $y$ values of point C are:

$x=\frac{1\times 10+2\times -8}{2+1}=\frac{10-16}{3}=\frac{-6}{3}=-2\\y=\frac{1\times -2+2\times 4}{2+1}=\frac{-2+8}{3}=\frac{6}{3}=2$

Therefore, the point that divides the line AB in the ration 2 : 1 is $C(-2,2)$