Final answer:
The coordinates of point K that divides the segment from J(4,1) to L(8,11) in the ratio of 3 to 1 are (7, 8.5) .
Step-by-step explanation:
To find the coordinates of point K that lies along the directed line segment from J(4,1) to L(8,11) and partitions the segment in the ratio of 3 to 1, we can use the formula for finding a point that divides a line segment into a given ratio:
K(x,y) = ((x1*m2 + x2*m1) / (m1 + m2), (y1*m2 + y2*m1) / (m1 + m2))
Where J is (x1,y1) = (4,1), L is (x2,y2) = (8,11), and the ratio is m1:m2 = 3:1.
Calculating the x-coordinate of K:
Kx = ((4*1) + (8*3)) / (3+1) = (4 + 24) / 4 = 28 / 4 = 7
Calculating the y-coordinate of K:
Ky = ((1*1) + (11*3)) / (3+1) = (1 + 33) / 4 = 34 / 4 = 8.5
Thus, the coordinates of point K are (7, 8.5).