Question

If P, Q and R are three points on a line and P lies between Q and R, then which of the following is always true?

• A. $PQ+QR=PR$
• B. $PR=QR-QP$
• C. $QP=\frac{QR+PR}{2}$
  
• D. $QP=\frac{QR-PR}{2}$
  

Answer 1

The correct option is B $PR=QR-QP$

Given that P, Q and R are three points on a line and P lies between Q and R.


Then it implies that QP + PR will coincide with the line segment QR.
By using Euclid's fourth axiom, which states that things which coincide with each other are equal to each other, we have:
$QP+PR=QR$
$\Rightarrow PR=QR-QP$
Hence, the correct answer is option (b).