Question

The point K lies on the segment JL.

Find the coordinates of K so that the ratio of JK to KL is 5 to 2.

J (-7,2)

K( ?,?)

L(28,-12)

Answer 1

To find the coordinates of point K on the segment JL, we can set up two equations using the ratio of JK to KL. Solving these equations will give us the coordinates of K, which are (22.17, -7.33).

Step-by-step explanation:

To find the coordinates of point K, we need to use the concept of ratios. Let's say the coordinates of point K are (x,y).

Using the ratio of JK to KL, we can set up two equations:
5 = (x - (-7)) / (28 - x)
2 = (y - 2) / (-12 - y)

Multiplying both equations by their denominators, we get:
5(28 - x) = x + 7
2(-12 - y) = y - 2

Simplifying the equations, we have:
140 - 5x = x + 7
-24 - 2y = y - 2

From the first equation, we get:
6x = 133
x = 22.17

Substituting the value of x in the second equation, we get:
-24 - 2y = y - 2
-3y = 22
y = -7.33

Therefore, the coordinates of point K are (22.17, -7.33).