Step 1
Given; A point T on a segment with endpoints D(1, 4) and F(7, 1) partitions the segment in a 2:1 ratio. Find T
Step 2
[tex]\begin{gathered} Ratio\text{ 2:1} \\ Let\text{ m=2, n=1} \\ x=\frac{mx_2+nx_1}{m+n},\text{ y=}\frac{my_2+ny_1}{m+n} \end{gathered}[/tex][tex]x_1=1,\text{ y}_1=4,\text{ x}_2=7,\text{ y}_2=1[/tex][tex]x=\frac{2(7)+1(1)}{3}=\frac{14+1}{3}=\frac{15}{3}=5[/tex][tex]y=\frac{2(1)+1(4)}{3}=\frac{6}{3}=2[/tex]Answer; T is
[tex](5,2)[/tex]
