Let's understand what it means when Q is the midpoint of line segment RS. A midpoint divides a line segment into two equal parts. This means that the distance from R to Q equals the distance from Q to S.
Now let's analyze each option systematically. We have four choices to consider. Option E states that 2RS equals QS. Option F says 2QS equals RS. Option G claims that half of RQ equals RS. And option H suggests that half of RS equals 2RQ. Let's identify the segments clearly on our diagram.
Let's test options E and F systematically. Since Q is the midpoint, we know that RQ equals QS, and both equal RS divided by 2. For option E, if 2RS equals QS, this would mean the entire segment doubled equals just half the segment, which is clearly false. For option F, if 2QS equals RS, this means 2 times RS over 2 equals RS, which simplifies to RS equals RS. This is true!
Let's check options G and H. For option G, half of RQ equals RS. Since RQ is RS over 2, half of RQ would be RS over 4, which clearly does not equal RS. This is false. For option H, half of RS equals 2RQ. We know that 2RQ equals RS, so this would mean RS over 2 equals RS, which is also false. Both options G and H are incorrect.
In conclusion, the correct answer is Option F: 2QS equals RS. This follows directly from the definition of a midpoint. When Q is the midpoint of RS, it divides the segment into two equal parts, so QS equals half of RS, which means 2QS equals RS. Remember this key property: for any midpoint, the whole segment equals twice either half-segment.