Question

The directed line segment, AB¯, contains the points A(−2,6)

Answer 1

Answer:

The coordinate of the point is; (0,2)

Step-by-step explanation:

The given line segment has points with coordinates  A(−2,6)

and B(4,−6).

We want to find a point (x,y) that divides this line segment in the ratio:

m:n=2:4

The x-coordinate of this point is given by;

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

We substitute $x_1=-2,x_2=4,m=2,n=4$

$\implies x=\frac{2*4+4*-2}{2+4}$

$\implies x=\frac{8-8}{6}=0$

The y-coordinate of this point is given by;

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

We substitute $y_1=6,y_2=-6,m=2,n=4$

$\implies y=\frac{2*-6+4*6}{2+4}$

$\implies y=\frac{-12+24}{6}=2$

The coordinate of the point is; (0,2)