Question

If R is the midpoint of QS, QR = 3x + 14 and RS = 7x-10, find QS.

Answer 1

If R is the midpoint of QS, that means the segments QR and RS have the same length.

Also, QS is the sum of the segments QR and RS.

So we have that:

`\begin{gathered} QR=RS \\ 3x+14=7x-10 \\ 3x-7x=-10-14 \\ -4x=-24 \\ 4x=24 \\ x=6 \\ \\ QS=QR+RS \\ QS=3x+14+7x-10 \\ QS=10x+4 \\ QS=10\cdot6+4 \\ QS=60+4 \\ QS=64 \end{gathered}`

So the length of QS is 64.