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ycow [4]
2 years ago
12

Point A is located at (5, 6) and point B is located at (8, −2) . What are the coordinates of the point that partitions the direc

ted line segment AB¯¯¯¯¯ in a 1:3 ratio?
Mathematics
2 answers:
spayn [35]2 years ago
6 0

Answer:

(6;3.33)

Step-by-step explanation:

To find the coordinates of the point that partitions in a 1:3 ratio, we use:

x=x_{1}+k(x_{2}-x_{1})\\y=y_{1}+k(y_{2}-y_{1})

Where k is the ration of partitions, \frac{1}{3} in this case.

Now, we replace all values:

x=x_{1}+k(x_{2}-x_{1})\\x=5+\frac{1}{3}(8-5)=5+\frac{1}{3}3=6

<em>So, the horizontal coordinate is 6.</em>

y=y_{1}+k(y_{2}-y_{1})\\y=6+\frac{1}{3}(-2-6)=6+\frac{1}{3}(-8)=3.33

<em>The vertical coordinate is 3.33.</em>

<em />

Therefore, the coordinates of the point that partitions the directed line segment AB in a 1:3 ratio is (6;3.33)

alekssr [168]2 years ago
5 0

Answer:

(6, 3 1/3)

Step-by-step explanation: Split this problem into x and y parts. In x direction, the length of the AB is (8-5)=3. So 1/3 from A would be 5+1/3(8-5)=6

In y, AB goes from 6 to -2, so the coordinate changes by (-2-6)=-8 units.

1/3 along this ling will be 6 + 1/3 (-2-6)=6-2 2/3=3 1/3

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