What are coordinates of the point on the directed line segment from (2,9) to (8,-3) that partitions the segment into a ratio of 1 to 3

Answer 1

Answer 2

(2,9) to (8,-3)

divide the line segment into a partition that's a ratio 1:3

(8-2)/(1+3) = 1.5

(-3-9)/(1+3) = -3

(2+1.5, 9-3)

= (3.5, 6)

check the answer, use the distance formula

from (2,9) to (8,-3) = sqr(36+144) = sqr180=3sqr20=6sqr5

from (2,9) to (3.5,6) = sqr(2.25+9) = sqr11.25=.5sqr45=.5sqr9sqr5= 1.5sqr5

from (3.5,6) to (8,-3) = sqr(20.25 +81) = sqr101.25=.5sqr45=.5sqr9sqr5= 4.5sqr5

1.5sqr5/4.5sqr5=1.5/4.5= 1/3

1.5sqr5 +4.5sqr5= 6sqr5

it might also help to draw a rough graph of the line segments, and plot the points

to visually see if the answer seems reasonable

some people might also come up with a different answer

(6.5,0) which also partitions the line segment into a ratio of 3:1, or 1:3 depending on

which direction you view the lines