1.

The middle point of the segment of the straight line joining the points `(p, q) and (q,-p)` is `(r/2, s/2).` What is the length of the segment?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`

Answer» Correct Answer - C
Two joining points are (p, q) and (q, -p)
Mid point of (p, q) and (q, -p) is `((p+q)/2, (q-p)/2)`
But it is given that the mid-point is `(r/s, s/2)`
`:. (p+r)/2=r/2 and (q-p)/2=s/2`
`implies 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))=(s^(2)+r^(2))^(1//2)`


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