The coordinates of point T (11/2 , 7/4).
A line segment is a part of a line that has two endpoints and a fixed length.
Here, Given the end points of the line segment are (1, 4) and (7, 1)
The ratio in which T divides the line = 3 : 1
We know that if a point P(x, y) divides a line segment in the ratio m : n
then, (x, y) = [tex](\frac{mx_{2}+nx_{1} }{m+n}, \frac{my_{2}+ny_{1} }{m+n} )[/tex]
where (x₁, y₁) and (x₂, y₂) are the end points of the line.
Let the coordinates of T be (x, y)
Substituting the values in equation (i), we get,
(x, y) = [tex](\frac{3X7+1X1 }{3+1}, \frac{3X1+1X4 }{3+1} )[/tex]
(x, y) = (22/4 , 7/4)
(x, y) = (11/2 , 7/4)
Thus, the coordinates of point T (11/2 , 7/4).
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