Answer: D. (2,-1)
Step-by-step explanation:
Given: In the diagram, point D divides line segment AB in the ratio of 5:3.
Since, line segment AC is vertical then the x coordinate of C will be same as A (2) and line segment CD is horizontal then the y coordinate of C will be same as D.
Coordinates of A = (2,-6)
Coordinates of B = (10,2)
Section formula: If a point P(x,y) divides a line segment MN with in ration m:n, then
[tex]x\ coordinate=\frac{mx_2+nx_1}{m+n}[/tex]
[tex]y\ coordinate=\frac{my_2+ny_1}{m+n}[/tex]
Using section formula, we have
The y coordinate of D =[tex]\frac{5(2)+3(-6)}{5+3}=\frac{10-18}{8}=\frac{-8}{8}=-1[/tex]
Thus, the coordinates of C =(2,-1)
