Respuesta :
Using proportions, it is found that the coordinates of point T are given as follows: T(5,2).
What is a proportion?
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, point T partitions the segment DF in a 2:1 ratio, hence:
[tex]T - D = \frac{2}{2+1}(F - D)[/tex]
[tex]T - D = \frac{2}{3}(F - D)[/tex]
This is applied for both coordinates, hence, for the x-coordinate:
[tex]x - 1 = \frac{2}{3}(7 - 1)[/tex]
x - 1 = 4
x = 5
For the y-coordinate:
[tex]y - 4 = \frac{2}{3}(1 - 4)[/tex]
y - 4 = -2
y = 2.
Hence, the coordinates of point T are: T(5,2).
More can be learned about proportions at https://brainly.com/question/24372153
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