Answer:
(4.75, 4)
Step-by-step explanation:
We are to find the coordinates of the point that partitions the directed line segment AB in 1:3 ration.
For this, we will use the following formula:
[tex] x = x_1 + k(x_2 - x_1) [/tex] , [tex] y = y_1 + k(y_2-y_1) [/tex]
where [tex] k [/tex] is the ratio of the first segment to the whole line segment so in this case, it will [tex] \frac{1}{4} [/tex].
So substituting the given values in the above formula to find the coordinates:
[tex] x = 3 + \frac {1}{4} (10-3) = 4.75 [/tex]
[tex] y = 6 + \frac{1}{4} (-2-6) = 4 [/tex]
Therefore, the coordinates of the point that partitions the directed line segment AB in a 1:3 ratio are (4.75, 4).
