Final answer:
To determine point P that divides line segment CD with endpoints C(7, -4) and D(-5, 4) in a 3:1 ratio, we use the section formula with m as 3 and n as 1, resulting in the fraction m/n being 3/1.
Step-by-step explanation:
To find the coordinates of point P that partitions line segment CD into a ratio of 3 to 1, we would use the section formula. In this case, point C has coordinates (7, -4) and point D has coordinates (-5, 4).
To find point P, we must apply the formula ((m*x2 + n*x1)/(m + n), (m*y2 + n*y1)/(m + n)), where (x1, y1) are the coordinates of C, (x2, y2) are the coordinates of D, and m:n is the given ratio.
The question asks for the value of m/n in the formula. Since the ratio given is 3:1, we take m to be 3 and n to be 1. Therefore, the fraction m/n that will be used in our calculations is 3/1.