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A swing set needs repair. The support bar that is at the middle of the A-frame is failing and must be replaced.
W
S
G
1. The legs of the frame SI and GI are each 5 ft long. If the crossbar WN intersects legs SI and Gl at their
midpoints, how far is point W from point S on the leg? Justify your answer and show all calculations.

Verified Answer :

GinnyAnswer

To determine the distance from point W to point S on the leg of the swing set frame, we can use the geometric properties of the frame setup.

1. Understanding the Configuration:
- The legs of the frame, SI and GI, are each 5 feet long.
- The crossbar WN intersects legs SI and GI at their midpoints.

2. Analyzing the Midpoint Concept:
- Since the crossbar WN intersects the legs at their midpoints, point W is exactly at the midpoint of leg SI.
- The midpoint of any segment is located exactly halfway between its endpoints.

3. Calculating the Distance:
- The total length of leg SI is 5 feet.
- Since W is the midpoint of SI, the distance from S to W is half of the total length of leg SI.

Thus:
\(\[ \text{Distance from point S to point W} = \frac{\text{Length of SI}}{2} = \frac{5 \, \text{ft}}{2} = 2.5 \, \text{ft} \]\)

Therefore, the distance from point W to point S on the leg is 2.5 feet. This result is justified based on the midpoint theorem, which states that the midpoint of a segment divides the segment into two equal parts.

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