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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. You must show all work to receive credit. ​

Sagot :

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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