Point e is located at (−1, 6) and point f is located at (3, 9) . what are the coordinates of the point that partitions the directed line segment ef¯¯¯¯¯ in a 3: 2 ratio? enter your answer, as decimals, in the boxes.

1 - 5,-2

2 - 34/3

3 - 40,34,6 4,-2

(1.4,7.8)

Step-by-step explanation:

E = (−1, 6)

F = (3, 9)

Displacement vector from E to F is

D = F−E = (3,9) − (−1,6) = (4,3)

E + 100% D should give F

(−1,6) + 1.0×(4,3) = (3,9)✔

The point that is 3/(3+2) = 60% of way from E to F is

P = E + 60% D = (−1,6) + 0.6×(4,3)

= (−1+2.4, 6+1.8) = (1.4,7.8)

(Length of EP) : (Length of PF) is supposed to be 3:2

(P−E) = (1.4,7.8) − (−1, 6) = (2.4,1.8)

(F−P) = (3, 9) − (1.4,7.8) = (1.6,1.2)

||EP|| = √((P−E) • (P−E))

= √((2.4,1.8) • (2.4,1.8))

= √(2.4^2+1.8^2) = 3

||PF|| = √((F−P) • (F−P))

= √((1.6,1.2) • (1.6,1.2))

= √(1.6^2+1.2^2) = 2

||EP|| : ||PF|| = 3:2 ✔

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