Question

A point T on a segment with endpoints D (1, 4) and F (7, 1) partitions the segment in a 3:1 ratio. Find T.

A) T(3, 3)
B) T(5, 3)
C) T(2, 5)
D) T(4, 4)

Answer 1

The point T that partitions the segment with endpoints D(1, 4) and F(7, 1) in a 3:1 ratio is T(4, 4) .

Step-by-step explanation:

To find the point T that divides the line segment DF in a 3:1 ratio, we use the section formula:

`\[ T\left(\frac{{3x_2 + 1x_1}}{{3+1}}, \frac{{3y_2 + 1y_1}}{{3+1}}\right) \]`

Given the endpointsD(1, 4) and F(7, 1) we substitute these values into the formula:

`\[ T\left(\frac{{3 \cdot 7 + 1 \cdot 1}}{{3+1}}, \frac{{3 \cdot 1 + 1 \cdot 4}}{{3+1}}\right) \]`

Simplifying, we get:

T(4, 4

Therefore, the correct answer is T(4, 4) , and it partitions the segment in a 3:1 ratio.