Question

Line segment cd has endpoints at c( 7, -4) and d(-5, 4). we want to find the coordinates of point p so that p partitions cd into a ratio of 3 to 1. a. what will the fraction latex: \frac{m}{n} m n equal in our formula?

Answer 1

To find point P that partitions line segment CD with endpoints C(7, -4) and D(-5, 4) in a 3:1 ratio, we use the section formula with m/n equaling 3. The resulting coordinates are P(-2, 2).

Step-by-step explanation:

The question is about partitioning a line segment CD with endpoints C(7, -4) and D(-5, 4) into a ratio of 3:1. To find the coordinates of point P that achieves this partition, we use the section formula. In this case, if we let m be the first number in our ratio (3) and n be the second number in the ratio (1), the fraction m/n will equal 3/1 or simply 3. The coordinates of P can be calculated using the formula:

P(x,y) = ((mx2 + nx1)/(m + n), (my2 + ny1)/(m + n))

Substituting the given values and the ratio, we can find the coordinates of P. Here's the calculation involving these values:

Therefore, the coordinates of point P that partitions line segment CD in the ratio of 3 to 1 are P(-2, 2).