Question

Point M is on line segment \overline{LN} LN . Given LN=3x+3,LN=3x+3, LM=4x,LM=4x, and MN=2x,MN=2x, determine the numerical length of \overline{MN}. MN .

Answer 1

Answer:

2 units.

Step-by-step explanation:

It is given that point M is on line segment LN. So,

$LN=LM+MN$         (Segment addition property)

The given values are LN=3x+3, LM=4x, and MN=2x. Substitute these values in the above formula.

$3x+3=4x+2x$

$3x+3=6x$

Subtract 3x from both sides.

$3x+3-3x=6x-3x$

$3=3x$

Divide both sides by 3.

$1=x$

$x=1$

The value of x is 1.

Now,

$MN=2x=2(1)=2$

Therefore, length of MN is 2 units.