Question

the point k is the mid - point of jl. find the location of l.

Explanation:

Step1: Recall mid - point formula

If \(K\) is the mid - point of \(JL\), and the coordinates of \(J=x_J\), \(K = x_K\), \(L=x_L\), then \(x_K=\frac{x_J + x_L}{2}\). Here \(x_J=- 5\) and \(x_K = 6\).

Step2: Rearrange the formula to solve for \(x_L\)

Starting from \(x_K=\frac{x_J + x_L}{2}\), we multiply both sides by 2: \(2x_K=x_J + x_L\). Then we can express \(x_L\) as \(x_L=2x_K - x_J\).

Step3: Substitute the values of \(x_J\) and \(x_K\)

Substitute \(x_J=-5\) and \(x_K = 6\) into the formula \(x_L=2x_K - x_J\). So \(x_L=2\times6-(-5)\).

Step4: Calculate the value of \(x_L\)

First, \(2\times6 = 12\), and \(-(-5)=5\). Then \(x_L=12 + 5=17\).

Answer:

17