Question

If A is the midpoint of line segment PR, PA = 7x - 11, and PR = 8x +14, then what is the value of line segment AR?

Answer 1

Given that:

A is the midpoint of line segment PR.

PA = 7x - 11 and PR = 8x +14.

Solution:

Since A is the midpoint of line segment PR.

`PA=AR=7x-11`

Using segment addition property, we get

`PR=PA+AR`

`8x+14=(7x-11)+(7x-11)`

`8x+14=14x-22`

Isolate variable terms.

`14+22=14x-8x`

`36=6x`

Divide both sides by 6.

`(36)/(6)=x`

`6=x`

The value of x is 6.

Now,

`AR=7x-11`

`AR=7(6)-11`

`AR=42-11`

`AR=31`

Therefore, the value of line segment AR is 31 units.