Answer:
[tex]\text{Partition point at }\left(8\frac{3}{4},10\right)[/tex]
B is correct.
Step-by-step explanation:
We are given point A(5,4) and point B(10,12).
We need to find point which divides line segment AB into 3:1
Using section formula of coordinate system to find coordinate
Formula:
[tex](x,y)\rightarrow \left(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\right)[/tex]
where,
[tex]A(x_1,y_1)\rightarrow (5,4)[/tex]
[tex]B(x_2,y_2)\rightarrow (10,12)[/tex]
[tex]m:n\rightarrow 3:1[/tex]
Substitute into formula and find out partition point,
[tex]\text{Point: }\left(\frac{3\cdot 10+1\cdot 5}{3+1},\frac{3\cdot 12+1\cdot 4}{3+1}\right)[/tex]
[tex]\text{Point: }\left(\frac{35}{4},\frac{40}{4}\right)[/tex]
[tex]\text{Point: }\left(8\frac{3}{4},10\right)[/tex]
[tex]\text{Thus, Partition point at }\left(8\frac{3}{4},10\right)[/tex]
