Question

What are the coordinates of the point on the directed line segment from (5,5) to
(8,-4) that partitions the segment into a ratio of 1 to 2?

Answer 1

Answer:

$(x,y) = (6,2)$

Step-by-step explanation:

Given

$(x_1,y_1) = (5,5)$

$(x_2,y_2) = (8,-4)$

$m:n = 1:2$

Required

Determine the coordinate of the partition

This is calculated using:

$(x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})$

Substitute values for m,n,x's and y's

$(x,y) = (\frac{1 * 8 + 2 * 5}{1+2},\frac{1*-4 + 2*5}{1 + 2})$

$(x,y) = (\frac{18}{3},\frac{6}{3})$

$(x,y) = (6,2)$