Problem

7. On the line below, the Iength of $\overline{R S}$ is 8 centimeters and the length of $\overline{S T}$ is 14 centimeters. What is the distance in centimeters from the midpoint of $\overline{R S}$ to point $T$ ?
A. 4
B. 7
C. 11
D. 18
E. 22

Answer

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Answer

Final Answer: The distance in centimeters from the midpoint of \(\overline{R S}\) to point T is \(\boxed{18}\).

Steps

Step 1 :The length of line segment \(\overline{R S}\) is given as 8 cm.

Step 2 :The length of line segment \(\overline{S T}\) is given as 14 cm.

Step 3 :The midpoint of a line segment is equidistant from both endpoints. Therefore, the distance from the midpoint of \(\overline{R S}\) to point S is half the length of \(\overline{R S}\), which is \(\frac{8}{2} = 4\) cm.

Step 4 :The distance from the midpoint of \(\overline{R S}\) to point T is the sum of the distance from the midpoint to point S and the distance from point S to point T.

Step 5 :So, we need to add 4 cm to the length of \(\overline{S T}\), which is 14 cm. Therefore, the distance from the midpoint of \(\overline{R S}\) to point T is \(4 + 14 = 18\) cm.

Step 6 :Final Answer: The distance in centimeters from the midpoint of \(\overline{R S}\) to point T is \(\boxed{18}\).

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