Question

Consider the line segment below that is five feet long. Is Q the midpoint of PR? Justify your answer.

Answer 1

Q is not the midpoint of PR

Explanation:

see the attached figure to better understand the problem

we know that

If Q is the midpoint of PR

then

PQ=QR

substitute the given values and solve for x

`15x-2=5x+3\\15x-5x=3+2\\10x=5\\x=0.5`

Remember that

`PR=5\ ft` ----> given problem

`PR=PQ+QR\\PR=(15x-2)+(5x+3)`

substitute the value of x

`PR=(15(0.5)-2)+(5(0.5)+3)`

`PR=(5.5)+(5.5)`

`PR=11\ ft`

Compare with the given value of PR

`5\ ft\\eq 11\ ft`

therefore

Q is not the midpoint of PR