Question

Point O is on line segment NP‾\overline{NP}NP. Given OP=10,OP=10,OP=10, NP=2x,NP=2x,NP=2x, and NO=x+7,NO=x+7,NO=x+7, determine the numerical length of NO‾.\overline{NO}.NO.

Answer 1

Given:

Point O is on line segment NP.

OP=10, NP=2x, and NO=x+7.

To find:

The numerical length of NO.

Solution:

If point O is on line segment NP, then by segment addition property, we get

$NP=NO+OP$

$2x=(x+7)+10$

$2x=x+17$

Subtract both sides by x.

$2x-x=17$

$x=17$

The value of x is 17.

Now,

$NO=x+7$

$NO=17+7$

$NO=24$

Therefore, the numerical length of NO is 24units.