Question

in the figure below, k lies between j and l. find the location of k so that the ratio of jk to kl is 2 to 3. j is at -13, l is at 7, k is at ?. location of k : input box, try again buttons.

Explanation:

Step1: Find the distance between J and L

The coordinate of J is -13 and the coordinate of L is 7. The distance \( JL = 7 - (-13)=7 + 13 = 20\).

Step2: Determine the length of JK

The ratio of \( JK:KL = 2:3\), so the total number of parts is \(2 + 3=5\) parts. Each part has length \(\frac{JL}{5}=\frac{20}{5} = 4\). Then \( JK=2\times4 = 8\).

Step3: Find the coordinate of K

Starting from J (-13), moving 8 units towards L (since K is between J and L), the coordinate of K is \(-13+8=-5\).

Answer:

-5