PLEASE HELP WILL GIVE BRAILIEST AND 10 POINTSPoint A is located at (5, 4) and point B is located at (10, 12).What point partitions the directed line segment ​ AB¯¯¯¯¯ ​ into 3:1 ratio?(614, 6)(834, 10)(8, 5)(7, 11)

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]