First of all in the given question you have to write down the values of the total length of the line segment, PS=15. The length of the line segment, QR =3. Now you have to find the value of line segment RS. Because you know that the Q is the midpoint of the line segments PQ and QS must be equal. Therefore you can find out the length of the half of the segment using the midpoint. Subtract the value of QR from QS. Given that segment PS=15 and Q is the midpoint, you can conclude segment PQ=7.5 and QS = 7.5. Because 15 divide by 2 will give 7.5. Now given that the segment QR is 3 and you have just found that QS=7.5, so you can find segment RS by subtracting RS from QS that is, (7.5-3) = (4.5). Therefore 4.5 is the desired answer. That's it.