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Maslowich
3 years ago
7

find the coordinates of the point on the directed segment from (3,2) to (6,8) that divides it into a ratio of 1:3.​

Mathematics
2 answers:
egoroff_w [7]3 years ago
8 0

Answer:

  (3.75, 3.5)

Step-by-step explanation:

The weighting factors for the weighted average of the end points are the reverse of the length ratios.

For a 1 : 3 split, the first point is weighted by a factor of 3; the second point is weighted by a factor of 1. The weighted sum is divided by the total of the weights.

  (3(3, 2) +1(6, 8))/(3+1) = (9+6, 6+8)/4 = (3.75, 3.5)

Natasha2012 [34]3 years ago
3 0

Answer:

\fbox{\begin{minipage}{9em}Option d is correct\end{minipage}}

Step-by-step explanation:

<em><u>Given:</u></em>

Point A(3, 2)

Point B(6, 8)

Point C lies on segment line AB and divides AB into a ratio of 1 : 3

<em><u>Solve for:</u></em>

Coordinate of C

<em><u>Solution:</u></em>

Denote the coordinate of origin O(0, 0)

Point A(3, 2) => Vector OA(3 - 0, 2 - 0) or OA(3, 2)

Point B(6, 8) => Vector OB(6 - 0, 8 - 0) or OB(6, 8)

=> Vector AB = Vector OB - Vector OA = (6 - 3, 8 - 2) or vector AB(3, 6)

Point C lies on segment line AB and divides AB into a ratio of 1 : 3

=> Vector AC = (1/3) Vector CB, or

    AC/CB = 1/3

=> AC/(AC + CB) = 1/(1 + 3)

=> AC/AB = 1/4

=> AC = AB/4

=>  Vector AC = (1/4) Vector AB  = ((1/4)*3, (1/4)*6) = (0.75, 1.5)

=> Vector OC = Vector OA + Vector AC = (3 + 0.75, 2 + 1.5) = (3.75, 3.5)

=> C(3.75, 3.5)

Option d is correct!

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