Final answer:
To find the coordinates of point K on line segment JL in the ratio of 7:8, apply the formula for internal division. The coordinates calculated for K are (8, 5), corresponding to option A.
Step-by-step explanation:
The question asks us to find the coordinates of point K on line segment JL with given endpoints J (-5,-1) and L (19,9), where the ratio of JK to JL is 7:8. To find K's coordinates, we will use the concept of internal division in a given ratio.
We need to apply the formula for internal division which is given by:
K's x-coordinate = [(x1 × m) + (x2 × n)] / (m + n), where J is (x1, y1) and L is (x2, y2), and the ratio is m:n.
K's y-coordinate = [(y1 × m) + (y2 × n)] / (m + n).
After applying these formulas with m = 7 and n = 8, the coordinates of K are found to be (8, 5), which corresponds to option A.