Answer:
The correct option will be: D. (6, 2)
Step-by-step explanation:
Point [tex]S[/tex] divides the line segment [tex]YB[/tex] in a ratio of [tex]4:1[/tex]
Given that, [tex]Y(-10, 6)[/tex] and [tex]B(10, 1)[/tex]
If a point [tex](x,y)[/tex] divides a line segment with endpoints as [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] in a ratio of [tex]m:n[/tex] , then...........
[tex](x, y)= (\frac{mx_{2}+nx_{1}}{m+n},\frac{my_{2}+ny_{1}}{m+n})[/tex]
Here, [tex](x_{1}, y_{1})=(-10,6)[/tex] and [tex](x_{2}, y_{2})=(10,1)[/tex]
Also, [tex]m:n=4:1[/tex]
Now plugging the values, we will get........
[tex]x=\frac{4(10)+1(-10)}{4+1}= \frac{40-10}{5}= \frac{30}{5}=6 \\ \\ \\ y=\frac{4(1)+1(6)}{4+1}= \frac{4+6}{5}= \frac{10}{5}=2[/tex]
So, the coordinates for point S will be: (6, 2)
