A) \[[{{({{s}^{2}}+{{r}^{2}})}^{1/2}}]/2\]
B) \[[{{({{s}^{2}}+{{r}^{2}})}^{1/2}}]/4\]
C) \[{{({{s}^{2}}+{{r}^{2}})}^{1/2}}\]
D) \[s+r\]
Correct Answer: C
Solution :
[c] Two joining points are (p, q) and (q, -p) Midpoint of (p, q) and (q, -p) is \[\left( \frac{p+q}{2},\frac{q-p}{2} \right)\] But it is given that the mid-point is \[\left( \frac{r}{2},\frac{s}{2} \right)\] \[\therefore \frac{p+q}{2}=\frac{r}{2}\] and \[\frac{q-p}{2}=\frac{s}{2}\] \[\Rightarrow p+q=r\] and \[q-p=s\] Now, length of segment \[=\sqrt{{{(p-q)}^{2}}+{{(q+p)}^{2}}}\] (By distance formula) \[=\sqrt{{{s}^{2}}+{{r}^{2}}}\]
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