Question

1. Points P.Q & R are on a number line such that d(P,R)= 15, d(Q.R)= 5. Find d(P,Q) Considering all possibilities.​

Answer 1

Let's assume that point P is at $x$.

There are two possibilities for $\overline{PR}$,

• $\overline{PR}=15$
• $P(x)$

$\implies R(x-15)\text{ or }R(x+15)$

Also, there are two possibilities for $\overline{PQ}$,

• $\overline{QR}=5$
• $R(x-15)\text{ or }R(x+15)$

$\implies Q(x-20)\text{ or }Q(x-10)\text{ or }Q(x+10)\text{ or }Q(x+20)$

Thus, all the possible lengths of $\overline{PQ}$ are 10 or 20.