Final answer:
The point on the directed segment AB from A(7,-3) to B(-7,4) that divides it in the ratio 3:4 is found using the section formula and is calculated to be (1, 0).
Step-by-step explanation:
To find the point on the directed segment AB that divides it in the ratio 3:4, we can use the section formula for internal division in two dimensions. The section formula for a line divided in the ratio m:n is given by:
(x,y) = ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n))
Using A(7,-3) and B(-7,4) as our points with the ratio 3:4, we calculate as follows:
(x,y) = ((3*(-7) + 4*(7)) / (3 + 4), (3*4 + 4*(-3)) / (3 + 4))
(x,y) = ((-21 + 28) / 7, (12 - 12) / 7)
(x,y) = (7 / 7, 0 / 7)
(x,y) = (1, 0)
Therefore, the point that divides the directed segment AB in the ratio of 3:4 is (1, 0).