Question

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 directed line segment AB¯¯¯¯¯ in a 1:3 ratio?

Answer 1

`(6;3.33)`

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,
`(1)/(3)` in this case.

Now, we replace all values:

`x=x_(1)+k(x_(2)-x_(1))\\x=5+(1)/(3)(8-5)=5+(1)/(3)3=6`

So, the horizontal coordinate is 6.

`y=y_(1)+k(y_(2)-y_(1))\\y=6+(1)/(3)(-2-6)=6+(1)/(3)(-8)=3.33`

The vertical coordinate is 3.33.

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

Answer 2

(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