What are the coordinates of the points on the directed line segment from K(-5,-4) to L(5,1) that partitions the segment into a ratio of 3 to 2.

Let's say we seek P between K and L such that

KP:PL = 3:2

P is a bit closer to L; knowing that helps us keep our fractions straight.

The line from K to L parametrically is

(x,y) = (1-t)K + tL = K + t(L-K)

t=0 means right on K, and t=1 means right on L.  

We want t = 3/(3+2) = 3/5, which is in the right proportion, closer to L

K(-5,-4) to L(5,1)

P(x,y) = K + (3/5)(L - K) = (-5,-4) + (3/5)(5 - -5, 1 - -4) = (-5,-4)+(6,3) = (1, -1)

Let's check the coordinates separately; they should match:

KPx:PLx = (1- -5):(5 -1) = 6:4 = 3:2, good

KPy:PLy = (-1 - -4) : ( 1 - -1 ) = 3:2, good

(1, -1)

3/5

step-by-step explanation:

double number line is not a standard concept, so it must have been defined in your textbook. assume top line is numerator.