Question

Question 3: A point T on a segment with endpoints F(1, 8) and G (4, 1) partitions the segment in a 3:2 ratio Find T Express your answer as an integer or simplified fraction and show all workT (__, ___)

Answer 1

Given:

The endpoint is F(1,8) and G (4,1)

Line segment in a 3:2

Find-: Point "T"

Sol:

Point then line segment is m:n then,

$\begin{gathered} x=\frac{mx_2+nx_1}{m+n} \\ \\ y=\frac{my_2+ny_1}{m+n} \end{gathered}$

Endpoint is:

$\begin{gathered} (x_1,y_1)=(1,8) \\ \\ (x_2,y_2)=(4,1) \\ \\ m:n=3:2 \end{gathered}$

So point is:

$\begin{gathered} x=\frac{mx_2+nx_1}{m+n} \\ \\ x=\frac{3(4)+2(1)}{3+2} \\ \\ x=\frac{12+2}{5} \\ \\ x=\frac{14}{5} \end{gathered}$

Y value of point is:

$\begin{gathered} y=\frac{my_2+ny_1}{m+n} \\ \\ y=\frac{3(1)+2(8)}{3+2} \\ \\ y=\frac{3+16}{5} \\ \\ y=\frac{19}{5} \end{gathered}$

So, point T is:

$T(\frac{14}{5},\frac{19}{5})$