Question

Point N is on line segment \overline{MO}

MO
. Given MN=2x,MN=2x, NO=x-2,NO=x−2, and MO=2x+9,MO=2x+9, determine the numerical length of \overline{MN}.
MN
.

Answer 1

NO = 10

Explanation:

The segment addition theorem tells you ...

MN + NO = MO

Substituting the given expressions for these lengths, we have ...

x + 5x = 3x+6

3x = 6 . . . . . . . . . subtract 3x

x = 2 . . . . . . . . . . divide by 3

We can use this value to find the length NO:

NO = 5x = 5(2) . . . . substitute for x

NO = 10