Question

1. Find the measure of line LM if M is the midpoint of line LN and LM = 3x – 2 and MN = 2x + 1.

Answer 1

1. 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....

$3x-2= 2x+1\\ \\ 3x-2x= 1+2\\ \\ x=3$

So, the measure of LM will be: $3x-2=3(3)-2 = 9-2= 7$

2.  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: $(\frac{x+6}{2}, \frac{y-2}{2})$

Given that, the co ordinate of F  as (1, 3.5)

So,

$\frac{x+6}{2}=1 \\ \\ x+6=2\\ \\ x= 2-6=-4$

and

$\frac{y-2}{2}= 3.5\\ \\ y-2= 7\\ \\ y= 7+2 =9$

So, the co ordinate of point F will be (-4, 9)