Final answer:
The correct point T that divides the segment between points D (1, 4) and F (7, 1) in a 3:1 ratio has the coordinates T(5.5, 1.75), which is not listed in the provided options.
Step-by-step explanation:
The student is asking for the coordinates of a point T that divides the segment between points D (1, 4) and F (7, 1) in a 3:1 ratio.
To find point T, we can use the section formula:
T(x, y) = ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n))
Here, m:n is the ratio, which is 3:1, x1 and y1 are coordinates for point D, and x2 and y2 are coordinates for point F. Plugging the values into the formula, we get:
T(x) = ((3×7 + 1×1) / (3 + 1))
= (21 + 1) / 4
= 22 / 4
= 5.5
T(y) = ((3×1 + 4×1) / (3 + 1))
= (3 + 4) / 4
= 7 / 4
= 1.75
However, none of the given options match the calculated coordinates.
The correct point T should be T(5.5, 1.75)