Question

Line segment PQ is a directed line segment beginning at P(6,-5) and ending at Q(-2,4). Find point R on the line segment PQ that partitions it into the segments PR and RQ in the ratio 3:2.

a. (-1, 1)
b. (2, -3)
c. (4, -1)
d. (-4, 2)

Answer 1

To find point R on line segment PQ that partitions it into the segments PR and RQ in the ratio 3:2, use the section formula.

Step-by-step explanation:

To find point R on line segment PQ that partitions it into the segments PR and RQ in the ratio 3:2, we can use the section formula. The coordinates of point R can be found using the formula:

x-coordinate of R = ((2 * x-coordinate of Q) + (3 * x-coordinate of P)) / (2 + 3)

y-coordinate of R = ((2 * y-coordinate of Q) + (3 * y-coordinate of P)) / (2 + 3)

Substituting the given coordinates, we get:

x-coordinate of R = ((2 * (-2)) + (3 * (6))) / (2 + 3) = (-4 + 18) / 5 = 14 / 5 = 2.8

y-coordinate of R = ((2 * 4) + (3 * (-5))) / (2 + 3) = (8 - 15) / 5 = -7 / 5 = -1.4

Therefore, point R is approximately (2.8, -1.4).