Question

Given JL with J(9, 5) and L(5, 16), if K lies on IL and partitions it such that the ratio of JK to KL is 2:5, find the coordinates of K.

a. (7, 8)
b. (6, 10)
c. (5, 12)
d. (4, 14)

Answer 1

To find the coordinates of point K on the line segment JL, we can use the section formula. By finding the coordinates of the midpoint I and then applying the section formula with the given ratio, we can determine that the coordinates of point K are (6, 10).

Step-by-step explanation:

To find the coordinates of point K, we can use the concept of section formula. The section formula states that if a point P divides a line segment AB in the ratio m:n, then the coordinates of P can be found using the following formula:

x-coordinate of P = (nx-coordinate of A + mx-coordinate of B) / (m + n)

y-coordinate of P = (ny-coordinate of A + my-coordinate of B) / (m + n)

In this case, point I is the midpoint of JL, so we can find its coordinates by taking the average of the x-coordinates and y-coordinates of J and L. Then, using the section formula with the given ratio, we can find the coordinates of point K.

First, let's find the coordinates of I:

x-coordinate of I = (9 + 5) / 2 = 7

y-coordinate of I = (5 + 16) / 2 = 10.5

Now, let's find the coordinates of K:

x-coordinate of K = (2 * 7 + 5 * 5) / (2 + 5) = 6

y-coordinate of K = (2 * 10.5 + 5 * 16) / (2 + 5) = 10

Therefore, the coordinates of point K are (6, 10), which corresponds to option b.