Question

Given JL with (-5,-1) and L (19,9), if K lies on JL such that the ratio of JK to JL is 7:8, find the coordinates of K.

A) K (8, 5)
B) K (9, 6)
C) K (11, 7)
D) K (12, 8)

Answer 1

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.