Question

in the figure below, k lies between j and l. find the location of k so that ( jk ) is ( \frac{1}{2} ) of ( jl ). (j is at -31, l is at -5; k is a point between them with an unknown coordinate, and a box to enter the location of k.)

Explanation:

Step1: Calculate the length of JL

The coordinate of J is -31 and the coordinate of L is -5. The distance between J and L (JL) is calculated by subtracting the coordinate of J from the coordinate of L (since -5 > -31). So, \( JL = -5 - (-31) = -5 + 31 = 26 \).

Step2: Calculate the length of JK

We know that \( JK=\frac{1}{2}JL \). Substituting the value of JL we found, \( JK = \frac{1}{2}\times26 = 13 \).

Step3: Find the coordinate of K

To find the coordinate of K, we start from the coordinate of J and move towards L by the length of JK. The coordinate of J is -31, so we add JK to the coordinate of J (because we are moving towards the right on the number line where values increase). So, the coordinate of K is \( -31 + 13 = -18 \).

Answer:

-18