<u>1. </u> If M is the midpoint of line LN , then the length of LM and MN will be equal to each other.
Given that, LM= 3x -2 and MN= 2x+1
So, the equation will be....
![3x-2= 2x+1\\ \\ 3x-2x= 1+2\\ \\ x=3](https://tex.z-dn.net/?f=3x-2%3D%202x%2B1%5C%5C%20%5C%5C%203x-2x%3D%201%2B2%5C%5C%20%5C%5C%20x%3D3)
So, the measure of LM will be: ![3x-2=3(3)-2 = 9-2= 7](https://tex.z-dn.net/?f=%203x-2%3D3%283%29-2%20%3D%209-2%3D%207)
<u>2.</u> Suppose, the co ordinate of point G is (x, y)
Co ordinate of point J is given as (6, -2)
If point F is the midpoint of line GJ , then the co ordinate of F will be: ![(\frac{x+6}{2}, \frac{y-2}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx%2B6%7D%7B2%7D%2C%20%5Cfrac%7By-2%7D%7B2%7D%29)
Given that, the co ordinate of F as (1, 3.5)
So,
![\frac{x+6}{2}=1 \\ \\ x+6=2\\ \\ x= 2-6=-4](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B6%7D%7B2%7D%3D1%20%5C%5C%20%5C%5C%20x%2B6%3D2%5C%5C%20%5C%5C%20x%3D%202-6%3D-4)
and
![\frac{y-2}{2}= 3.5\\ \\ y-2= 7\\ \\ y= 7+2 =9](https://tex.z-dn.net/?f=%5Cfrac%7By-2%7D%7B2%7D%3D%203.5%5C%5C%20%5C%5C%20y-2%3D%207%5C%5C%20%5C%5C%20y%3D%207%2B2%20%3D9)
So, the co ordinate of point F will be (-4, 9)