Question

Point p is on line segment OQ. Given PQ=x+7,OP=4x-10,and OQ=4x, determine the numerical length of oq

Answer 1

Given:

Point P is on line segment OQ.

PQ=x+7,OP=4x-10,and OQ=4x.

To find:

The numerical length of OQ.

Solution:

Since, point P is on line segment OQ, so by segment addition property, we get

`OQ=OP+PQ`

`4x=(4x-10)+(x+7)`

`4x=(4x+x)+(7-10)`

`4x=5x-3`

`4x-5x=-3`

`-x=-3`

`x=3`

The value of x is 3.

Now,

`OQ=4x`

Putting x=3, we get

`OQ=4(3)`

`OQ=12`

Therefore, the numerical length of OQ is 12 units.