143k views
5 votes
A point T on a segment with endpoints D (1, 4) and F (7, 1) partitions the segment in a 3:1 ratio. How do you find T?

a) Use the midpoint formula
b) Use the slope-intercept formula
c) Use the distance formula
d) Use the Pythagorean theorem

User Nadeem
by
7.7k points

1 Answer

3 votes

Final answer:

To find point T which divides the line segment from D (1, 4) to F (7, 1) in a 3:1 ratio, calculate the weighted average of the endpoints' coordinates. The coordinates of T are found to be (5.5, 1.75).

Step-by-step explanation:

To find point T on a segment with endpoints D (1, 4) and F (7, 1) that partitions the segment in a 3:1 ratio, you need to use the concept of dividing a segment into a given ratio, which involves a mixture of the distance formula concepts and algebraic calculation. However, the most appropriate method to find the coordinates of T is by computing a weighted average of the endpoints' coordinates based on the given ratio.

The formula for finding the coordinates of T (x, y) in a ratio of m:n between points D (x1, y1) and F (x2, y2) is given by:

x = (mx2 + nx1) / (m + n)

y = (my2 + ny1) / (m + n)

In this case, the ration m:n is 3:1, so substituting the values we get:

x = (3*7 + 1*1) / (3 + 1) = (21 + 1) / 4 = 22 / 4 = 5.5

y = (3*1 + 1*4) / (3 + 1) = (3 + 4) / 4 = 7 / 4 = 1.75

Therefore, the coordinates of point T are (5.5, 1.75).

User Rahatur
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories