Question

If d(P, Q) + d(Q, R) = d(P, R) then it is said that point Q is between P and R. The betweenness is shown as ______. *​

Answer 1

Answer:

Q lies between P and R

Thus PR=PQ+QR

Now, we are given PQ=QR

Put QR=PQ

⇒PR=PQ+PQ

⇒PR=2PQ

⇒

2

1

PR=PQ

⇒PQ=

2

1

PR

Hence proved.

Answer 2

If $d(P,Q)+d(Q+R)=d(P,R)$, then it is said that point $Q$ is between $P$ and $R$. The betweenness is shown as

$\bold{d(P,Q)\:or\:d(Q,R)=\dfrac{1}{n}d(P,R)\:;\:n>1}$.

Explanation:

• Since $d(P,Q)+d(Q,R)=d(P,R)$ with the statement that the point $Q$ lies between $P$ and $R$, we must take that the point $Q$ lies at any point on $PR$.

• This can be shows with the condition: $d(P,Q)\:or\:d(Q,R)=\dfrac{1}{n}d(P,R)$ where $n>1$.

• Here $n\neq 1$, because if $n=1$, then the point $Q$ lies on one of the two extremities of $PR$.