Question

A point T on a segment with endpoints D(1, 4) and F(7, 1) partitions the segment in a 2:1 ratio. Finds T.

Answer 1

In geometry, points are used to divide segments into subsegments using partitions or ratios.

The position of T is: (5,2)

Given that:

$D = (1,4)$ ---- $(x_1,y_1)$

$F = (7,1)$ ---- $(x_2,y_2)$

$m : n = 2:1$

The position of T is calculated using the following line ratio formula

$T = \frac{1}{m+n}(mx_2 +nx_1,my_2 +ny_1)$

So, we have:

$T = \frac{1}{2+1}(2 * 7 +1 *1,2 * 1 +1 * 4)$

$T = \frac{1}{3}(15,6)$

Expand

$T = (\frac{1}{3}*15,\frac{1}{3}*6)$

$T = (5,2)$

Read more at:

brainly.com/question/3148758

Answer 2

Answer:

( 5 , 2)

Step-by-step explanation:

The coordinates  of T  can be found as

[ 1 + (2/3)(7 - 1)  ,  4 + (2/3)(1 - 4) ]  =

[ 1 + (2/3)(6) , 4 + (2/3)(-3) ]  =

[ 1 + 4.   4  - 2 ]  =

( 5 , 2)