Question

7. Given M is the midpoint of LN, Mark this on the diagram.If LM = 6x + 22 and MN = 9x - 20. What is the value of x? What is the length of LM ?What is the length of LN ? Please show all work24 -X=LMNLM=LN =

Answer 1

Explanation

Midpoint refers to a point that is in the middle of the line joining two points. ... Further, if a line is drawn to bisect the line joining these two points, the line passes through the midpoint.

Therefore, we can say that the midpoint divides the line LN into two equal parts. Hence,

$\begin{gathered} LM=6x+22 \\ MN=9x-20 \end{gathered}$

This gives

$\begin{gathered} 6x+22=9x-20_{} \\ 6x-9x=-22-20 \\ -3x=-42 \\ x=\frac{-42}{-3} \\ x=14 \end{gathered}$

Therefore LM is

$LM=6x+22=6(14)+22=106$

Also LN

$\begin{gathered} LN=6x+22+9x-20 \\ =15x+2 \\ =15(14)+2 \\ =212 \end{gathered}$

Answer:

$\begin{gathered} x=14 \\ LM=106 \\ LN=212 \end{gathered}$